text:
Is there any way to rehabilitate the "junk rare" Lost In The Woods?
I've really been enjoying the incredible Innistrad set, and advance previews of Dark Ascension (on the Wizards official site and elsewhere) have been living up to it so far.  However, I had to do a double take when I read the text of this rare, Lost in the Woods, it seemed so bad:

Lost in the Woods, 3GG [Enchantment]
Whenever a creature attacks you or a planeswalker you control, reveal
the top card of your library.  If it's a Forest card, remove that
creature from combat.  Then put the revealed card on the bottom of
your library.

I feel like the ability on this card would be bad if it Fogged all creatures on a Forest reveal, not just one creature.  I feel like the card would still be bad if it cost G and you could cast multiples of it in early turns - but as an expensive late game card, it seems totally unplayable.
Obviously it's a "flavourful" card that will never see competitive play.  But come on, surely no Magic card can be completely without actual play value?  This is the hardest card to think of a good use for that I've come across in ages, though - can anyone else think of a great combo or other strategy for making Lost In The Woods a halfway decent addition to a deck?

Do you get to use the ability twice if two creatures attack you in the same turn?

@Pat Yes, it triggers for every creature that attacks you. You reveal as many cards as creatures attacking you. The defender decides on the trigger order.

@Hackworth How do you get "the defender decides on the trigger order"?

@AlexP Game rule 101.4c. 101.4c If a player would make more than one choice at the same time, the player makes the choices in the order written, or in the order he or she chooses if the choices aren't ordered.

or better: 405.3 If an effect puts two or more objects on the stack at the same time, those controlled by the active player are put on lowest, followed by each other player's objects in APNAP order (see rule 101.4). If a player controls more than one of these objects, that player chooses their relative order on the stack.

@Hackworth I totally forgot that the player who owned Lost in the Woods would be the defender in this case. Oops. >.>

Bad card or not, the flavor is pretty awesome.

I'm not actually going to vote this way, but until DKA actually comes out there's an argument for this being too localized.  By the time you can play with it, there may be a card that justifies it.

@Ian, I was thinking that: maybe a card reading something like "whenever you reveal a card from your library, do x" would suddenly make for sense of this.  Even if such cards are in the pipeline, though, I can't really see Lost In The Woods benefitting much... I would love to be wrong though!

IMHO it would be cool to have a tag for this kind of question "rehabilitating junk MTG cards"

I would have agreed with you that this card could never see competitive play, it turns out that Lost in the Woods was used by several players at Pro Tour Honolulu: http://www.wizards.com/magic/magazine/article.aspx?x=mtg/daily/eventcoverage/ptdka12/friday_plays

Haha, yes, it certainly makes for an audacious sideboarding strategy in Limited!  I'm not sure that actually counts as a "real" use for the card though - as the article pretty much points out, it loses to anyone who prepares for it (so you still have to be able to win at least one game by fair means), and even occasionally just  has to scoop to random cards like Gravepurge.  Plus how tedious a game would this be to actually play?  I think I'd just say to myself "it might work, but you know, I came here to play Magic..."

Top player Luis Scott Vargas gave it a 0.0 rating out of 5 in his Dark Ascension Limited review recently, and I'm inclined to agree with that still!

@thesunneversets In fairness, I think at least 1 point of that is LSV marking down this card for being a rare that's not Zombie Apocalypse. ;)

This is a terribad card beyond redemption.
As already pointed out, it's too expensive to bring into play to have noticeable effect; also it's too weak and unpredictable an effect to be really useful. It doesn't even have useful side effects like only sending the forests to the bottom, it's just random.
Another problem is that it's pretty much restricted to mono-green decks because of the GG casting cost and because it works on forests only. Mono-Green, however, is typically all about stomping your opponent, not about gaining board control. This is a board control card, no color is worse in getting board control than green, and this card will do exactly nothing to change that.
That being said, the best card I can think to combo with this is good old Sensei's Divining Top, but if you, with a green-heavy or mono-green deck, have to rely on this card to win the damage race, then your deck has quite a bit of a problem anyway.

With Sensei's Divining Top you could say that putting all cards (forest or not) on the bottom is a feature since you can remove other bad spells or lands if you wish. But as you pointed out, it's way too situational and expensive for just putting a few cards on the bottom of your library.

I'm accepting this as the correct answer because, despite some entertaining and/or optimistic suggestions for ways to use this rare from other people, I think the bolded first line of this answer remains by far the best one-line summary!

It's a rather awful card with one very limited application that only really works in draft.
Here's a deck that can win a game or two (likely only games, not matches) in Dark Ascension draft and sealed:

1x Lost in the Woods
45x Forest

Transform into it for game 2 after you're sure they don't have enchantment removal or enough mill or burn to bypass it.
Mulligan until you get Lost in the Woods in your opening hand.
Play a Forest a turn (you're guaranteed to draw one) until you can cast Lost in the Woods.
Win the game by running your opponent out of cards, TurboFog-style.

This trick is rather fragile, but it was apparently good enough to win a few games on the Pro Tour! (As discussed here and here.)
Importantly, it's a trick that costs almost nothing in draft: you can draft a normal deck in any colors and randomly twelth-pick this single junk rare to give yourself an entire alternate strategy to swap into. That's the very lowest possible investment for a transformational strategy, well worth the potential to "steal" a game or two out of nowhere.

Beyond that... no, not really.
As a defensive card, it doesn't really compare to staples like Propaganda and Spike Weaver.
Benefits:

It's a permanent, of a pretty durable kind.
Protects your planeswalkers, too. A lot of older defensive enchantments don't.
It's not a damage-prevention effect.
Multiples stack nicely.
You control how the triggers are stacked. If you know what's in first few cards of your library, you can use Lost in the Woods to stop the biggest threat.
The creatures it removes from combat don't become untapped as a result.

Drawbacks:

Only works on forests, not any land. This is quite prohibitive.
Cmc 5. If this were much lower, Lost in the Woods might still be worth it as a card that a ramp could drop to slow down an aggro opponent.

Basically the problem is that it's too slow for 60-card Magic but a singleton copy doesn't do very much for you in Commander. The card can be improved by synergy with stuff like Sensei's Divining Top, but that's like saying Siege Mastodon is more playable with Black Lotus.
Beyond the fog effect, this card does do something else, though: it lets you go through a bunch of your deck. With something like Future Sight on the field, you can take advantage of the individual resolution of the triggers to cycle through a chunk of your library looking for stuff to cast. The major downside is that making effectively use of this requires not only a Future Sight effect, but also the ability to play most of your stuff at instant speed. It's much easier to set up the same combo with Top.

Haha, I really like your creative idea with the 46-card fog deck. Which decks do you think it's best against? I feel like any deck with white would be problematic.

It's very fragile. The trick is to find an opponent who's not running enchantment removal (and give them no reason to side it in during game 1). Silverchase Fox maindeck would definitely screw you up. So does a moderate amount of mill, though (or burn, in an aggressive enough deck).

Note that this deck was used by several players at Pro Tour Honolulu: http://www.wizards.com/magic/magazine/article.aspx?x=mtg/daily/eventcoverage/ptdka12/friday_plays

The pro-tour honolulu article is dead.  But, this link: https://www.magicmadhouse.co.uk/articles/2014/11/tims-top-fives-the-five-most-ridiculous-things-seen-at-a-pro-tour/ and this link: http://www.starcitygames.com/magic/generallimited/23636_Finding_Your_Way_Out_Of_The_Woods.html discuss it.

@John Thanks, John! $%$^# Wizards messing up their old articles every two to three years.

There are actually several rare cards that have nearly no play value. Look at One with Nothing for another example of a bad rare.
There are several reasons why cards like this are created though.  Mark Rosewater, a designer for MTG has a couple of well-written articles that explains why bad rares are created. Read When Cards Go Bad and Rare, but Well Done.

I agree with your point, but not quite with your example. One With Nothing has several, quite useful applications in the right deck: (1) guaranteed, instant-speed Hellbent practically anytime, (2) helps Threshold, (3) Madness cards (4) Dredge cards, just off the top of my head

This is very true. It's winter time right now and my house is cold, but thanks to One with Nothing I was able to keep a fire going all night. And just a few weeks ago, I'd run out of toilet paper...

+1 for humor :) Magic cards as toilet paper, though? I'd rather be forced to build a deck around Lost in the Woods.

Now with RTR we get Overgrown Tomb then in gatecrash Stomping Ground will be back.
Id totally run a deck with 4 slaughter games, 4 Lost in the woods, 4 OGTombs and 4 Stomping grounds (+ forests)
Clearly the idea is to play a lost in the woods, then slaughter games yourself for lost in the woods. Leaving only forests in your deck. Ask your opp if they have ench removal, Then simply draw go for 30 minutes.
Sure it wouldnt win, like anywhere. But it would be pretty damn funny when you did get that guy who didnt have 20 burn in his deck/no ench removal/no other win con.

I like the way you think :)

There are viable uses for something like this.
In a birthing pod deck, you're not going to be casting all that many creatures. At the very least, you can afford to not cast creatures, because you're still getting tons of them, probably a lot of tokens or other card advantage with all the battlefield triggers.
Assuming you have any decent acceleration, you're looking at podding into a turn 4 solumn simulcrum and a 4 drop, a turn 5 this and podding into an acedic slime, and a turn 6 5-or-6 drop and podding into a titan or wurmcoil.
I'm not suggesting its the best fit, but in a green heavy birthpod deck, it could be fairly useful.
There's also a card called Scouting Trek that says "Search your library for any number of basic land cards. Reveal those cards, then shuffle your library and put them on top of it." So obviously this would be very useful. (Note it does not say reveal the order in which you put them on top of your library, so the attacker does not know which one will hit what.)
You could also use it in conjunction with Cellar Door - it puts the bottom card of your library in your graveyard to put a 2/2 token in if the card was a creature. If you have a lot of creatures that can be cast from the graveyard (which is very popular here) this is an easy way to know what's on the bottom of your library.
And when you consider that they made lords uncommon in this set, they had to put something as rares... and if they didn't make this a rare they would (typically) increase its cost further, which would make it even less playable.
Admittedly the card would be better if it had a 3 or 4 cost, or if the creatures didn't untap during the next untap step or something like that.
tl;dr there are a couple ways to use this card that would be fun, particularly in a casual or sealed environments given the right circumstances. It's not a horrid card. I'd still take this over magnetic mine...

+1 for the Scouting Trek idea, though I can't imagine it paying off in a real deck.  I still feel like a 5cc card where we're having to jump through all sort of hoops to find a way it wouldn't be an actively terrible addition to a deck is probably worthless.  Certainly it's hard to imagine there aren't better 5 drops to add in its place, in any given deck...

True, in most constructed environments, I'd agree. I think in limited where games drag out this could be useful. I also think in casual environments (which they must also make cards for) this is a very fun card. It's also dripping in flavor :)

Well one deck idea I had was Lumber Mill. You run 4 Lost in the Woods and 4 Sands of Delibrium to do mill work since the deck will have 52 forests for Losts ability and enough mana for Sands ability to be effective. You would have a 65-70 percent chance of winning with it in standard.  The only decks that oppose against this deck would be Burn and Control but with RTR it is mostly aggro and it would work extremely well in the format for now.

Hmm, can't they potentially kill you in their first 5 turns while you do nothing waiting to be able to play Lost In The Woods?  It's a nice thought but I'm just not sure it's as close to an auto-win as you say (though it probably is against some decks, for sure).

Setting aside surviving the first 5 turns, I'm not sure how you're guessing a 65-70% win chance. Chances of drawing at least one of four Lost in the Woods in your first 12 cards are 60%. Even if you draw it, what about counterspells? What about enchantment destruction? Direct damage? These things aren't played in standard?

Uses for this card:
1) In Commander format for a mono-green deck;
2) The only way to make this a viable fog would be to force a Forest to the top of the deck; There are some ways to do this (mostly all of them are blue):

Ponder and Brainstorm effects;
Cards with scry like Augury Owl, Cryptic Annelid, Crystal Ball, ...;
Other cards that manipulate the top of Library like Ancestral Knowledge, Crystal Seer, Descendant of Soramaro, Aven Fateshaper;
Congregation at Dawn/Worldly Tutor to fetch Dryad Arbor;

3) Some effect that could use the knowledge of the last card in your Library like Cellar Door (as @thesunneversets pointed out);
4) Some effect that could use the knowledge of the top card in your library like Druidic Satchel, Delver of Secrets, Abundance, ...;
5) Don't forget that simply filtering through your Forests isn't that bad either. To play this card you have to spend 5 mana, which probably is already enough to run your deck so it helps you make sure you're not drawing blanks!
Seems like I misread the card (kudos to @Hackworth) so #4 and #5 don't work.

It doesn't just filter through your Forests, though, does it?  It sends whatever's at the top of your deck to the bottom of the deck, after showing your opponent what you're playing and (once in a while) saving you a few points of damage... Cellar Door uses the knowledge of the bottom card of your library, but Cellar Door/Lost in the Woods is hardly what you'd call a killer combo!

It only sends the card to bottom if it's a Forest. Which means if it isn't you'll be revealing the same card for all opponents creatures (unless you shuffle in response to one of the triggers) and they will all attack as normal.

Actually, after reading it again, I'm not sure if all cards are sent to bottom or only the Forests ._.

The revealed card gets sent to the bottom in any case.

In most cases the card is pretty bad, but I have a commander deck that plays it and works pretty well.
The commander I play Lost in the Woods with is Sasaya, Orochi Ascendant. This deck plays more lands than most decks and apart from 5 to 6 non-basic lands they are all Forests. Lost in the Woods can give me some time while I have some mana already, but not enough mana (or other resources) to kill my opponents with.


text:
Has there ever been any use for Lich?
Is there any good deck which uses Lich?
Sure, there is some very corner-case where having it in the battlefield will help you, such as if you have fewer life than permanents, and you are about to kill your opponent, but even in that case, you'd rather have a card which actually kills him, rather than this…
So: is it just a terrible card, or is or has there been any actual use?

The question is if there is a deck where it would make sense to put this card and not another one, NOT if there is a strange corner case where if you magically happened to have this card in your hand, it would make sense to play it.

This question seems incredibly questionable, and I would argue primarily opinion based. Literally every card in mtg can have a use.

@Waterseas I disagree. If it's so easy, you should be able to answer it.

I can give several examples where it could be relevant just off the top of my head. Lich + Laboratory Maniac + Life gain. Lich + Gray Merchant of Asphodel. Whether it is answerable or not is completely beside the point.

@Lohoris The added paragraph sounds combative. I would recommend rewording the entire question to the tune of "Are there any good decks that use Lich" or "How do you go about building a Lich deck"?

The linked 'lich' page has a 'view decks with lich' link: http://magic.tcgplayer.com/db/deck_search_result.asp?CardName=Lich&partner=MAGCINFO  have you looked through these decklists for an answer to your question?

@ColinD I never noticed that link, I'm looking at it now, thanks

Voted to close as primarily opinion based. It looks like the author wants a single example to convince him that the card is not terrible. It seems argumentative to me.

@Rainbolt and why is this in-topic, instead? It's exactly the same question (about a different card, ofc).

@Lohoris I can't tell you how many times I have been challenged on a close vote by users who cite other questions exactly like it. The existence of other opinionated questions does not excuse yours. I suggest you read How many questions on meta have asked, “Why can't I ask this question when that question is open”?. Also, look at the accepted answer on that question. It starts with (in bold), "This is a terribad card beyond redemption." Also, the question is three years old.

@Rainbolt so are you claiming that if the answer is "it's bad" it is in-topic, while if there are uses then it becomes off-topic?

@Lohoris No, I am not.

@Lohoris Suggestion: If you're going to be argumentative about reasons for voting to close, I would recommend taking your discussion to a discussion.

@Rainbolt Ahem. Note that there's also another answer that explains how to play that same terribad card at a Pro Tour.

In response to your update: whether or not one should substitute card A for card B in a deck will depend on your reasons. From a flavor perspective (see Alex P.'s answer), it may make complete sense to include Lich over "better" cards that are more likely to win games.

So sad to see this question on hold.  These are some of my favorite type of questions.

@John These types of questions are what mtg forums are for, not stack exchange.

Why was Lich created?
I think this is the real subtext of your question: why does Lich exist?
I think to understand Lich, you've got to put it in context: it's a flavor-first design from Alpha. Lich is, first and foremost, supposed to feel like lichdom in fantasy stories, particularly Dungeons & Dragons: undeath, power and immortality at a grave price.
One thing the card does well is establish a big theme for black: trading away your life for power in near-suicidal ways.
However, one of Alpha's biggest shortcomings is that it's all over the map about what cards are worth as a resource. On the one side, you've got cards like Ancestral Recall. On the other, you've got Lich.
So, Lich is an early attempt to do something pretty tricky in Magic, and it is, by most standards, a misfire (part of what hurts it now is errata which forces "cards" to "nontoken permanents," thereby cutting off many strategies for artificially inflating your permanent count). You can see attempts to refine this design in various cards like Nefarious Lich and Necropotence.
What can you do with Lich?
Nearly any card this weird is fodder for at least a few combos.

Lich turns life gain into cards. This is very pretty powerful because it's easier to gain 1 life than to draw a card, but any deck built around this as an enabler is going to be rather fragile.

Lich sets your life total to zero. You can try to abuse this with various cards, such as Mirror Universe.

Lich makes life loss that isn't damage meaningless to you. (Look at Ad Nauseam for instance).  Note that you can't pay life, either, though.

Lich will kill its controller when it goes to the graveyard. You could try to set up some Donate-style combos with this, but it's pretty bad because you need other cards to ensure you don't die at zero life.

Is it good in a competitive environment?
No.
But most Magic cards aren't.

No mention of Mirror Universe in the "What can you do with Lich?" section?

@Powerlord "Such as Soul Conduit." >.>

Right, but the reason I mentioned Mirror Universe is that it was a well known and highly effective strategy in Alpha/Beta... the same sets that contained Lich in the first place.

@Powerlord Mirror Universe is originally from Legends, so several years after Alpha/Beta.

@bwarner alpha came out in July '93, Beta in October '93, Legends in June '94, so people playing Alpha/Beta at the time most definitely were likely to be playing Legends cards as well.

As a note, look at the new Lich's Mastery, which is a "fixed" variant of Lich + Nefarious Lich.

@Samthere Huh. They finally made a Lich card that works well. Cool.

LIch + Platnium Angel + Donate!

You can use Lich with Death's Shadow or Magus of the Mirror or Repay in Kind.

Lich, at a cost of BBBB, is too expensive to be part of a competitive tournament combo given it's only playable in Legacy (compare to the 6 mana win with Painter's Servant + Grindstone) or Vintage (compare to the 4 mana win with Time Vault + Voltaic Key).  There is also the big downside that you can lose the game to a Disenchant or have to sacrifice all of your lands to a big swing from an agro deck.  But there are a lot of cool things you can do with it in casual play (possibly with Platinum Angel as backup).
Lich is actually a really interesting card for it's combo potential.  Most combo cards have one ability you can combo off of.  Lich has three.  These have been partially discussed by @VolleyJosh and @AlexP, but I want to go more into detail.  Here they are:

It let's you be alive with 0 (or less) life.  This means you can use it to kill a player using cards that give your life total to someone else like Mirror Universe, Magus of the Mirror, and Repay in Kind.  It also makes Death's Shadow a 13/13 for one mana.
It lets you turn life gain into card draw.  This can create a powerful draw engine with cards like Essence Harvest, Consume Spirit, and Sapling of Colfenor.
It lets you ignore any non-damage loss of life .  Because you don't die for having less than 0 life, and the only penalty from Lich is for taking damage, other sources of life loss don't matter.  This combos great with Delaying Shield, which converts all of that pesky damage into irrelevant life loss.  This also negates the downsides of cards like Ad Nauseam, Dark Confidant, Reanimate, and Sapling of Colfenor.

I don't think the mana cost is the reason it isn't good in competitive play.

@JoeW As shown in point 1, Lich can be used in a 2-card win combo that only requires one color of mana.  What is different about Lich's win combo from other "competitive" ones?  It's either the mana cost or the risk of losing the game that comes with playing Lich.  I've rearranged the answer a bit to make this clearer.

How many other multi card win combos also set your opponent up to be able to win the game with a single card? The fact that there are so many cards that can cause the lose of lich and thus the game is a bigger issue then the mana cost especially in a mono color deck.

Lich is an extreme card advantage card. If the battlefield is balanced - no advantage to either player in attacking - and your opponent is not playing direct damage, and you have any repeatable life gain at all, you will draw your whole deck in short order.
It isn't a card you could drop into any Black deck; it requires you to construct a deck around it. But a good combo deck is designed to reproduce the conditions that are good for the combo. So the disadvantages are mitigated and you have a powerful card drawing engine.

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text:
In Guillotine, do Noble abilities work from the score area?
The card Clerical Error has the text:

Choose a player.  Collect any noble of your choice from that player's
score pile.  That player then chooses any other noble from your score
pile and collects it.

The noble Robespierre has the text:

The day ends after you collect this noble.  Discard any nobles
remaining in line.

According to this thread on their interaction:

Clerical Error would work just fine, but end the day and discard all
nobles in line if used to get Robespierre from someone else's score
pile.

This seems to imply that noble abilities continue to work from the score area, which seems consistent with nobles like the Palace Guards, whose abilities must work from the score area.  So, two-fold question:

Does this mean that if I use Clerical Error to collect someone else's Rival Executioner ("Collect the top noble of the noble deck after you collect this noble"), I get that ability?  (I'm guessing yes)

Why doesn't the Master Spy ("After each action card is played, move this card to the end of the line.") move to the end of the line from your score area if anyone plays an action?

To put it differently, what rules framework can we construct for Guillotine about what types of abilities work in what zones of play to get the desired behavior?

Part 1
Yes, you do get an extra noble from the deck when taking someone else's Rival Executioner with Clerical Error.  If that collected noble has a "when you collect" ability, it will trigger as well.
Rationale: Based on the ruling regarding Robespierre, we can conclude that nobles with a "when you collect" ability trigger when that noble is collected, no matter what method.  This includes during the phase of the turn when you collect the first noble in line, the card Clerical Error, the Fast Noble, the Rival Executioner.  This does not include the card After You, which reads "Put the noble at the front of the line into another player's score pile."  Only and all abilities with the specific word "collect" trigger "when you collect" abilities.

Part 2
A strict interpretation of the Master Spy seems to indicate he should move to the back of the line from the score area.  The action cards that manipulate an arbitrary noble all have text saying explicitly that they only modify nobles in line, while the Master Spy's ability does not.  For example, Public Demand has the text:

Move any noble in line to the front of the line

Fled to England has the text:

Discard any noble in line.

Meanwhile, the Master Spy simply says to move him to the back of the line, with no restriction that he must be in line.
The only proper defense for the Master Spy not moving to the line from the score area is that the word "move" only applies to nobles in line.  The extra in line clause on Public Demand is an extraneous clarification.  The actions that cause cards to change zones never say "move".  They say "place" if the noble is coming from the score area or "add" if it is coming from the deck.  Examples:
Missed:

Choose a player. That player must place the last noble he or she collected at the end of the line.

Extra Cart:

Add 3 nobles from the noble deck to the end of the line.

Consequently, the Master Spy only moves to the end of the line while he is in line.
(Credit to Gregor for some of the reasoning here).

To answer your first question, the answer is yes. All nobles that have effects that trigger on collection would have their effects happen again.
For your second question I believe that there is typically a 'to the best of your(the cards) ability' with most games. So with Master Spy, he can't move to the end of the line because he is not in the line ... also he had his head cut off, but that's something entirely different.

There are plenty of action cards that put nobles that are not currently in the line at the end of the line.  There is no rule preventing the Master Spy from moving to the end of the line from the score area.  This wouldn't be a problem if triggered abilities didn't work from the score area but the first part establishes the precedent that they do.

I'm making my argument based off of how I feel most of these games work. And to be fair, the cards that put nobles from a players pile back into the line expressly say that they do so. In the end, its your game and you should play it the way you think it should. I totally get the word 'collect/collected' and its interaction, it makes a ton of sense to me, but the Master Spy would be rejoining the line triggering outside of the line and wouldn't be able to move to the back of the line because he is no longer apart of the line. I don't see a FAQ ruling on it, so I'm just going with my gut.

I agree with the conclusion that the master spy doesn't go to the line from the score area because of his ability. But what rules framework can we infer onto Guillotine that gets us this result?  (See this answer for an example: http://boardgames.stackexchange.com/a/24127/9999).  Consistency of rules trumps authorial intent.

I think the word move implies a reordering, not adding and reordering. Generally, movements in line are relative to the initial placement of a card (move it forward or backward x places in line), which clearly doesn't affect cards that aren't in line.

With Master Spy, the movement doesn't depend on where he is in line, but the key word move is the same. To be wholly consistent, it could be phrased "move this card from where it is in line to the end of the line", but I think the authors chose a reasonable, natural-sounding phrasing instead (not even assuming it was a deliberate choice).

@Gregor this looks like the foundation of a good answer.  You should post it as such.  Also do you have supporting card text?

No, that was all shooting from the hip--which is why I only made it a comment.

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text:
What can I do about uncounterable spells?
I cast Fling, sacrificing my only creature to kill my opponent.  My opponent responds with Last Word, which will win the game the other way.  Last Word says "This spell can't be countered."  What else can I do about it besides countering it to prevent my plans from being foiled?  (I'd really like to have the last word here.)

Historic Note: before of the April 2018 rules change, uncounterable spells with targets used to actually have different wording (still visible on the printed cards) implying that they still could be countered.  For example, Last Word said:

Last Word can't be countered by spells or abilities.

Meanwhile Akroma, Angel of Fury said:

Akroma, Angel of Fury can't be countered.

Please don't put spaces just inside your [mtg:] formatting - instead of [mtg: Fling], write [mtg:Fling]. It can break the link, at least for those of us using SOUP to fix our auto link feature.

Since the link still does not go directly to the page, it would probably be better to just link directly to the card page. I made that change here.

@murgatroid99 You should totally get SOUP. The fix in it takes us straight to the page. :D

Even if it helps, we should optimize for the common visitor, not the power user who knows about stuff like that.

Since you answered your own question, I felt comfortable editing the title to ask what you appear to be looking for. Feel free to roll it back if I was wrong.

Am very confused why the title was changed.

@Waterseas I believe the edit was based on Rainbolt's understanding of the answer (and the relevant rules) as explained in http://boardgames.stackexchange.com/q/24143/409; if the ideas in that question had been correct the edit would've made sense.

An interesting example is Gilded Drake which contains Oracle text "This ability can't be countered except by spells and abilities." since the ability targets but needs to sacrifice if it fails.

@murgatroid99 I think optimizing for the common visitor, in this case, means "Yell at the devs to patch the system so [mtg] links aren't broken constantly anymore."

@AlexP Sure, that would definitely be the best. But I don't have control over that, so in the meantime I think the second best solution is to fix links so that they work for all visitors within the system as it exists.

"What else can I do about it?" Don't have winning the game be dependent on a single card?

@Acccumulation This is an update of the question to still be relevant in light of the 2018 rules change.  The question was, and remains, about things that can be done in response to uncounterable spells.

There is now no way to "counter" an uncounterable spell, but you can achieve the same effect by preventing it from resolving.  The easiest way to do this is to cause all of its targets to be invalid:

608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process.  If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard.

There are 2 ways to do this:

Change the target of the uncounterable spell.  You can prevent Last Word from resolving by changing it's target, such as via Redirect.  By using Redirect to change Last Word to target Redirect, Last Word will not resolve, as described in this ruling:

If you cast Redirect targeting a spell that targets a spell on the stack (like Cancel does, for example), you can’t change that spell’s target to itself. You can, however, change that spell’s target to Redirect. If you do, that spell won’t resolve when it tries to resolve because Redirect will have left the stack by then.

Make the targeted object a new object.  If the targeted object is a spell, you can use Ertai's Meddling will bring your spell back later when their spell is no longer on the stack.  If the targeted object is a permanent (such as a creature targeted by Inescapable Blaze), exiling it and returning it to the battlefield (such as with Momentary Blink) will cause it to become a new permanent and no longer targeted by the spell.

As far as uncounterable spells in general (like Thrun, the Last Troll), there are a few other ways you can deal with them while they are on the stack (none of which are technically countering):

You can exile the spell, such as with Time Stop, Mindbreak Trap, or Ertai's Meddling.
You can return the spell to their hand, such as with Venser, Shaper Savant.
You can tuck the spell with Commit.
You can steal the spell with Æthersnatch or Commandeer.
In multiplayer games, defeating a player removes all of that player's spells from the stack.  Door to Nothingness is the ultimate counterspell.

Finally, in the case described in the question about Last Word and Fling, you could Twincast the Fling, and have a copy that is not countered.  The copy of Fling uses the additional costs paid for the original spell.

Historic Note: before the April 2018 rules change, uncounterable spells like Last Word had wording like "Last Word can't be countered by spells or abilities."  Rule 608.2b used to have the spell be countered by game rules if all its targets were invalid on resolution.  The only functional difference is for cards that care about what has been countered, notably Multani's Presence

608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. ... The spell or ability is countered if
  all its targets, for every instance of the word “target,” are now
  illegal.

Why aren't you able to change Last Word's target to itself?

@GendoIkari A spell is not a legal target for itself.

@murgatroid99 Thanks; found it in rule 114.4.

Killing an opponent removes all of his/her spells from the stack. That is relevant to multiplayer games.

@Hackworth Door to Nothingness is my favorite counterspell.

Since the Dominaria Comprehensive Rules changes it does no longer say "by spells or abilities" because rule 608.2b has been changed. To quote:

608.2b
  One of the Dominaria changes was saying that spells can't be countered, dropping "by spells and abilities." This means that spells that fizzle* shouldn't actually be countered anymore—they just go to their owner's graveyard and don't resolve, but they don't use the keyword action of "counter" to do so. This is a nonfunctional change with the exception of one weirdo: Multani's Presence.
*Yes, fizzle. I'm a linguistic descriptivist, and people want a shorter way to express this, so I whole-heartedly endorse saying "fizzle" in non-technical contexts (for example, not in the Release Notes, where I use many more words to express this). We very briefly considered resurrecting it as an official term and rejected it.

Apart from the answers already given, the card Commit // Memory from Amonkhet allows you to put the spell second from top of their library.

Yeah, this is a way to get around "Can not be countered" as it does not counter the spell, it just relocates it.

With regards to your question

Also, why does Last Word have this extra clause where Akroma, Angel of Fury does not?

You have to remember that

Card design standards change over time.
The oracle text on the gatherer is the official text on the card.

If you look at the oracle text, both cards now say

This spell can't be countered.

The original reason for this difference was a spell with targets would be countered by the game itself when all targets were made illegal, and they had to still word it to allow this automatic countering.

As for why they are now the same, this is no longer the case, spells with all targets made illegal are not longer countered by game state, they are put into the graveyard without resolving, which is different from countering, so they don't need the ability to be countered by game state anymore.


text:
Netrunner Stalemate
A stalemate is possible in Netrunner if all of the following are true:

Sufficient agenda points have been taken out of play that neither player can get to 7 points, such as through forfeiting agendas or Glenn Station
The corp has sufficient recursion that they won't lose from drawing from an empty R&D, such as a scored Hades Fragment, or Reclamation Order + Archived Memories + Rework
The corp has no way to flatline the runner

I assume in a tournament, the game would be a draw due to the time constraint of tournament play.  Is there a formal rule for how to handle this situation in general?

Of the cards listed here for 2, only Hades Fragment will prevent the corp from decking out. The other two add cards to HQ not R&D, to the hand, not the deck. Other options do exist such as Whampoa Reclamation and Museum of History, but they are vulnerable to runner trashing.

@Andrew Added Rework, which should make it work

Archived memories to return reclamation order, 2 reclamation orders to return archived memories and reworks rework to put archived memories and other reworks into R&D? Might work would have to game it out, see if there is a way to sustain that, I doubt it due to the number of clicks and credits required.

@Andrew you only need to play Rework once a turn to stay alive indefinitely.  Going through a complete cycle, you play two Reclamation Orders (getting Rework x3 each time), play 6 Reworks, play three Archived Memories (getting Reclamation Order x1 each time), play one Reclamation Order (getting Archived Memories x3), and click for credits three times (to pay for Reclamation Order).  This is 18 clicks (6 turns), and gives you 6 shots of Rework, meaning you are drawing exactly as fast as you are replenishing R&D.  A single econ operation (such as Hedge Fund) could make it more efficient.

I think the closest rule that could arguably be applied is the one regarding infinite loops. From the NISEI Comprehensive Rules Document:

10.10. Infinite Loops
10.10.1. If a mandatory infinite loop is created (a player cannot choose to stop resolving the loop) then the player who is resolving the loop chooses a number. The loop instantaneously resolves that many times, and then ends. Example: The Runner runs into a rezzed Wormhole. The only other piece of ice that is rezzed is a Wormhole, and so a mandatory infinite loop is created where each the Wormholes’ subroutines resolves the other. The Corp chooses how many times this loop occurs, say 2,157 times, and then the Runner continues the run.
10.10.2. If an optional infinite loop is created (a player can choose to stop resolving the loop) during a run, then the Runner must jack out unless another card ability prevents them from doing so. If the Runner cannot jack out, then it is the Corp’s
responsibility to end the loop by letting the Runner continue the run.

The same text can be found in the last published FFG Rule Reference (v1.1).
I suppose an argument could be made that if such a stalemate situation occurs and it can be known to both players that there is no way to end the game, it could be treated as an optional infinite loop, which would mean the Corp would be compelled to break it (by choosing not to Hades Shard a card back into R&D and therefore losing by being decked/milled).
However, the rule above specifically talks about infinite loops which can occur in the context of a single run, rather than game states which cannot produce a result in either players' favour. Additionally, applying this rule as described above clearly gives an advantage to the Runner (although I would personally argue this is fine against any Corp trying to force a draw through infinite recursion).
So I think the short answer is that no, there isn't a specific ruling which deals with this (extremely unlikely) situation. But I'd be interested to hear from anyone else who knows otherwise.
Edit: jakodrako (co-creator of ANCUR and current NISEI Rules Manager) has stated here that the infinite loop rules are one of the areas on their list of things to investigate, so he's definitely aware of this.

What's interesting is that in all situations I have found, the corp is prolonging the game indefinitely through choosing  to use optional abilities (such as Hades Fragment).  This is actually decent precedent saying that the corp must at some point chose something different.

I haven't played in a while... Is it possible for both players to know (1) and (3)? Or would there be a reliance on one player claiming that both (1) and (3)are true?

It would be possible for both players to know (1), as the number of agenda points in a deck is defined based on the deck size, so once enough points have been seen and somehow removed, both players could know they cannot win on points. As for (3), this would be possible for both players to know once the Corp had played through their entire deck so it was visible to both players and each had subsequent turn just consisted of the Corp shuffling a card from Archives into R&D, taking a mandatory draw of that card and then doing whatever with the rest of their turn.

However, there is another consideration - whether the Runner has any cards or actions which could force the Corp to draw in addition to their mandatory draw.

Looking at the tournament rules here it talks about when a game is not won before 'going to time' :-

If victory
  has still not been achieved after the final turn, then the player
  with the highest number of agenda points is the winner of the
  game. If players have the same number of agenda points, then
  the higher seed wins the game.

Seeding is defined earlier in tournament rules as:-

Each player’s order of finish in the preliminary
  rounds determines his or her seeding in championship play: the
  player who qualifies with the most prestige in the preliminary
  rounds will play against the player who qualified with the least
  prestige in the preliminary rounds, the player with the secondmost
  prestige will play against the player with the second-least
  prestige, and so on. Ties are broken by strength of schedule, and
  then by random chance

I don't think this answers the question, as the OP acknowledges that in a tournament they would expect such a game to go to time, but rather is asking what rule (if any) could actually be used to deal with this situation in general, outside of a game going to time in a tournament situation.

This is a good case that a game that ends in a stalemate goes to whoever has more agenda points.  However, in the event that is still tied, I don't think there is a good analogue to "higher seed" outside of a tournament context.

@3N1GM4 It does apply because OP comments that the game would be a draw when going to time, which is not actually how organized play works for netrunner, an undecided game at the end of rounds will award a modified win, as said here, based on points or seed if possible, it's very rare for an actual netrunner draw


text:
Does priority matter in Magic?
When does priority actually matter in magic?  I have been playing Magic since Time Spiral and have never once seen the rules for priority matter.  I've never heard a question from a player about a game situation to which the answer was, "Oh, well it's right here in the rules for priority."
Let me elaborate.  Most other games handle questions of precedence (I want to do this but my opponent wants to do something conflicting) with a system of priority.  Magic handles questions of this type with the stack.  Here are some examples:

What tap effect has precedence?
I have a 2/2 and I want to play Giant Growth on it while my opponent wants to kill it with Lightning Bolt?  Resolved by the stack.  Priority doesn't actually matter here.  It's not a question of who has the option to act first, it's about who does act first, and because the person that acts first in this situation loses, the solution (given both players run Telepathy) is for both players to pass and the game to move on to the next step or phase.  But this isn't a quirk of priority, this is that the Nash Equilibrium given perfect information and how the stack works is for neither player to cast his/her spell.
I want to cast Silence on my opponent during his/her upkeep but he/she wants to cast Lightning Bolt on me first.  Sure, a player get's priority on his/her turn before other players, so he/she has the option to cast a spell before I can cast Silence, but it doesn't matter!  Since this all happens during the upkeep, the spell I want to cast has to be instant speed anyways, so it can be cast in response to Silence while Silence is on the stack.  Since Silence only takes effect on resolution, what order it and another spell are cast in won't change either spell's resolution (unless the other spell is a counterspell).  In almost all situations, Silence only changes the ability for the player to cast things post-upkeep.

In all of the above situations, the stack is what determines what happens.  Players priority in putting things on the stack doesn't matter since in the above cases (and the overwhelming majority of cases I've seen), as it is the ability to react that matters, not the ability to act first.
So, given how the stack works, does priority actually matter in Magic?  If so, what types of situations are the rules for priority needed to actually determine what happens?

For reference, here are the rules for priority:

116.3. Which player has priority is determined by the following rules:

116.3a The active player receives priority at the beginning of most steps and phases, after any turn-based actions (such as drawing a card
  during the draw step; see rule 703) have been dealt with and abilities
  that trigger at the beginning of that phase or step have been put on
  the stack. No player receives priority during the untap step. Players
  usually don't get priority during the cleanup step (see rule 514.3).
116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
116.3c If a player has priority when he or she casts a spell, activates an ability, or takes a special action, that player receives
  priority afterward.
116.3d If a player has priority and chooses not to take any actions, that player passes. If any mana is in that player's mana pool, he or
  she announces what mana is there. Then the next player in turn order
  receives priority.

116.4. If all players pass in succession (that is, if all players pass without taking any actions in between passing), the spell or ability
  on top of the stack resolves or, if the stack is empty, the phase or
  step ends.

Your Giant Growth example only makes sense if each player can see the other's hand, so it can't really be generalized. If they can't, then priority does matter because it will determine which plays their spell first.

@murgatroid99 The Giant Growth vs Lightning Bolt example is actually a WotC endorsed example of how the stack works.  Priority is basically irrelevant for it.  If I use Giant Growth first, you respond with Lightning Bolt; if you use Lightning Bolt first, I respond with Giant Growth.  I can pass priority whether I know what's in your hand or not.  Who casts first in this situation is usually determined by who needs the effect of their spell more, not by whose turn it is.  The Telepathy example was merely to illustrate optimal play.

The point I'm trying to make is that it's a good example of how the stack works, and that priority only doesn't matter because Telepathy was added to the mix. On each side, optimal play is different if the players don't have perfect information. And, if you're the active player and you pass priority, your opponent can pass priority and you miss the opportunity to cast Giant Growth because the step ends.

@murgatroid99 Please post an answer.  Your discussion has fallen beyond appropriate use of the comments section.

A common real life example: It practically guarantees a use of your Planewalker's loyalty ability before your opponent can kill it. See here for details.

@Zags I am questioning the validity of a statement you made in your question. I'm not answering the question in these comments, and putting these comments in an answer would be improper.

@murgatroid99 Sounds like an answer involving the relation of player action to hidden information to me.  But the analysis of how that actually plays out has been subtle enough that I haven't had too look up rules on priority in almost a decade of playing Magic.  I'd love to see an answer on the subject.

@Zags, Re "so he/she has the option to cast a spell before I can cast Silence, but it doesn't matter!" Actually, it does matter. They must cast it before you cast Silence. Otherwise you could simply not cast Silence and then they wouldn't be to cast in their Upkeep at all.

Did you misread what I said? The Active Player must cast first or risk not being able to cast at all. (Nothing to do with the other spell being Silence)

The point is that if active player passes priority in their upkeep instead of casting Lightning Bolt, then non-active player can pass priority instead of casting Silence and then nobody gets to cast anything during the upkeep.

@murgatroid99 Both players declining to act isn't a use of priority, it's both players declining to use priority.  Please post an answer if you would like to describe a situation where priority matters to what actions a player can take.  That's what the question is asking for.  Claiming that the examples in the question are actually examples of where priority matters sounds like a great basis for an answer, given the question is asking whether or not priority matters.

Declining to act is called "passing priority". You can't decline to "use priority", any more than you can decline to use the stack, or phases. If that's actually what you meant, then you seem to be misunderstanding something important about priority. And finding out what exactly the asker understands about their question is one of the most important use of comments.

@murgatroid99 "what types of situations do the rules for priority actually determine what happens?"  Players declining to take actions available to them in a part of a turn causing that part of the turn to the end is hardly specific to the rules of priority in Magic.  That's more in the category of "how boardgames work" than "how priority works in Magic"

Yeah, I read the question. I'm trying to understand what baseline to start an explanation from. You said "Both players declining to act isn't a use of priority, it's both players declining to use priority." What did you mean by that statement? What do you think rule 116.3d means?

@murgatroid99 I think I can verbalize it. Most priority passes can be "covered up" with shortcuts, sometimes even nonverbally. In which specific situations would shortcuts not work? This is why I voted to close the question as Too Broad. There are an arbitrarily large number of such situations.

@murgatroid99 Here's another way to think about it: what categories of situations exist in which a group of experienced board game players who had read all of the rules of Magic except for those governing priority would need to read the priority rules to understand how to proceed in a given situation?

@Rainbolt As my own answer should indicate, there are actually not that many.  There only appear to be two additional classes of circumstance categories being discusses in comments beyond those covered in my answer

You're making it even more complicated, and you still haven't answered my question: you seem to be misunderstanding how priority works at some basic level, and I'm trying to understand how you think it works. And, in that light, the completeness of your answer is suspect.

@murgatroid99 I understand just fine how priority works.  I've been certified as a Magic rules advisor multiple times.  My point about the priority rules is I've never seen them matter.  I've never gotten a question from a player to which the answer was, "oh, well it's right here in the rules for priority".  So, the question is, what types of situations would cause the rules for priority to matter in resolving a dispute?

And you still haven't answered my question: why did you say "Both players declining to act isn't a use of priority, it's both players declining to use priority." and why did you think that was a meaningful response to my description of the Lightning Bolt/Silence situation?

@murgatroid99 If I haven't answered your question, it's because I don't know what your question is.  The rules for priority govern which player has "priority" (the literal English word) to act.  A player not acting is a player refusing to exercise precedence in acting first, namely refusing a benefit allotted to him or her under the rules of priority.  Priority governs who has precedence in putting things on the stack.  If no one puts things on the stack, then no one has exercised their priority rights.

OK, this is what I was getting at. The English word "priority" doesn't have the same meaning as the priority rules in Magic, and using both meanings together is confusing. The important difference is that when you pass priority, you aren't just giving away the right to go first; you are also giving up your opportunity to cast something before the step ends. It's not a benefit that you can choose to ignore, it's an ordering.

@murgatroid99 You're not giving up the ability to cast something before the step ends.  You're only giving up the ability to cast something before the step ends conditional on the other player doing the same.  This is why I mention Nash Equilibria in the question.  Dictating who must choose to pass first is irrelevant if neither player wants to act first.

Let us continue this discussion in chat.

@murgatroid99 I added a prototype section on priority breaking an imperfect information situation in my answer. feel free to expand on it

Priority can matter, but only in rare corner cases.  Here are the main types of situations where priority matters.  Some of these are pretty obscure.

Split second cards
It's your turn.  You have in hand Dark Depths and Vampire Hexmage for the infamous Marit Lage combo.  Your opponent has Sudden Death in hand.  Can you summon Marit Lage?  The answer is yes.  You retain priority through playing Dark Depths and casting Vampire Hexmage, then your opponent gains priority while Hexmage is on the stack (which is still too early to cast Sudden Death on it), but then your opponent cannot respond again between the Hexmage resolving, entering the battlefield, and you activating its sacrifice ability.  As the active player, you can retain control through this entire process.  That said, if you were putting the Hexmage onto the battlefield on your opponent's turn through Aether Vial, they would be able to Sudden Death it before you could use its ability because they have priority.
If instead your plan is to win via Chance Encounter + Frenetic Efreet, you can still do it facing a Sudden Death if it is your turn and you play Chance Encounter first.  After the Efreet enters the battlefield, you have priority and retain it through as many activations of its ability as you want.  You can have a billion activations of its ability on the stack by the time your opponent has the option to Sudden Death it, giving you near statistical certainty that you will have enough counters on Chance Encounter to win.
The reason split second cards matter with priority is that they temporarily change how the stack works.  Instead of a player being able to respond at any time, they can't respond until the split second card has finished resolving, meaning when you can cast them matters since players cannot react with other spells or abilities once they are cast.

Sorcery speed abilities (such as planeswalker abilities)
When a planeswalker spell resolves, assuming it was the bottom spell on the stack and cast by the active player (so not cast using Vedalken Orrery or the like), the active player has the option to activate one of it's abilities before anyone else can do anything.  This is important because if someone else could do something, they could Lightning Bolt your planeswalker before you could use one of its abilities.  This pretty much only matters with planeswalkers because their abilities are sorcery speed.  Almost all other activated abilities of permanents are instant speed.  Those that aren't also benefit from priority.  This is anything with the text "Activate this ability only any time you could cast a sorcery." such as Aggravated Assault.  Basically, if you have a permanent enter the battlefield under your control, you can put one of its sorcery speed abilities on the stack before anyone else can kill or destroy the permanent.
The exception to this is if the card with a sorcery speed ability triggers an enter the battlefield ability, in which case the stack will not be empty when you gain priority and players will be able to use instant speed removal before you can use its abilitiy.
Also in this category are the ability to trigger abilities with sorcery speed cards, such as the situation in this question.  If the active player has just cast Kor Spiritdancer and it resolves and doesn't trigger any enter the battlefield abilities, the active player will be able to cast an Aura and consequently trigger the Spiritdancer's ability before the other player has the chance to play instant speed removal.

A change in casting eligibility as a result of a non-stack action (such as paying a cost, activating a mana ability, or unmorphing a creature)
You are playing a mill deck against a burn deck.  Your opponent has Searing Blaze in hand and you are at 1 life.  Meanwhile, your opponent has three cards left in his/her library, and they are all copies of Lightning Bolt.  You have Altar of Dementia on the battlefield and a beefy creature in hand.  Who wins?
This matters includes, but also goes far beyond, priority.  First, Searing Blaze requires that you have a creature on the battlefield for it to be cast.  The requirement is just for casting; the creature need not be there on resolution since as long as any of a spell's targets are still legal, the spell will resolve.  Additionally, sacrificing a creature to the Altar is part of the cost for the altar, and so the sacrifice doesn't use the stack.  Consequently, there is an action that doesn't use the stack that changes whether or not another action can be put on the stack.  It's a fairly rare situation, but it is one where priority matters.  If it is your turn, your creature can enter battlefield and then be sacrificed to the altar without your opponent getting priority.  By the time he/she has priority, the creature is already in the graveyard, and so Searing Blaze cannot be cast.

Retaining priority after playing a land
This is also going to be a bit contrived.  You have some creature that you need to give double strike in order for you to win.  You have Assault Strobe and a Mountain in hand, and several Mountains on the battlefield.  Your opponent has Mana Short.  Because of priority, they cannot stop you from casting Assault Strobe.  If they cast Mana Short before your main phase, you can just play the Mountain on your main phase and then cast Assault Strobe with it.  Meanwhile, if they wait, you retain priority after playing the land, and so can still cast Assault Strobe before they cast Mana Short.  The first chance they have to cast Mana Short during your main phase is in response to Assault Strobe.  Basically, this just means that Mana Short should be played before your opponent's main phase and that it doesn't deprive them of mana sources they get after that point, but this isn't exactly news.
As is the case for the sorcery speed abilities, if the land entering the battlefield triggers an ability, the stack won't be empty when you receive priority, so your opponent will have a chance to use Mana Short before you can cast Assault Strobe since sorceries can only be cast when the stack is empty.

Breaking the symmetry of hidden information
This is one introduced in comments and is perhaps the hardest to formalize.  Take the example in the question where a player is attacking with a 2/2 and has Giant Growth while the defender has Lightning Bolt.  It is now the declare blockers step, the last time to cast spells before combat damage.  If neither player knows about the other's threatened instant, than each player is eager to cast his/her card but whoever does so first loses the interaction.  Here, that the active player must chose first is a disadvantage because it causes the active player to be the one to make the bad decision rather than the non-active player.
That said, the application of priority rules here is only relevant if players are using a low degree of short-cutting (namely the non-active player waits for explicit verbal confirmation that the active player is not acting during the declare blockers step before announcing "I do this during the declare blockers").  In addition, no player trying to win will invoke priority rules here if he or she is erroneously skipped; the ability to respond is far more valuable.  As a final point to why this situation is particularly rare, both players must have to have basically equal willingness to take an action that is disadvantageous given full information.  For this to actually be the case requires fairly specific setups of both game board and player psyche, and occurs rather rarely in practice.

Multiplayer
If multiple players want to respond to a particular event (such as by countering a mass-removal spell), whoever is earlier in priority will be at the disadvantage of acting first.  Perfect information in this situation doesn't help.  The first player with the option to counter the spell cannot know for certain the true priorities of the next player with the option to counter it.  The first player must chose whether to counter the spell or risk it going uncountered where the second player has the leisure of only needing to counter it if the first does not.

Vialing in the Hexmage doesn't matter, you had priority to activate the ability so you have priority when it finishes resolving.
116.3c If a player has priority when he or she casts a spell, activates an ability, or takes a special action, that player receives priority afterward.

@diego – Actually, 116.3b handles the case for priority after a spell or ability resolves (giving it to the active player). 116.3c is for responding to casting your own spell or activating an ability.

Doh, you're right, apparently I can't read today :)

I think you might've missed possibly the most common time it matters: combat tricks. For example, say you attack with a creature and want to cast Giant Growth on it to help finish off your opponent, but are worried they might have a Doom Blade. You're the active player, so you get priority first, and have to decide whether to cast your spell without knowing whether the creature is going to die, while your opponent can sit back and wait to see if you pump it before they spend their removal spell.

@Jefromi this is exactly one of those cases where priority doesn't matter.  If priority worked differently, and they had the option to play their removal spell first and declined to, they could still cast it in response to your buff ability.

@Zags Nope, it matters. Yes, they can kill it either way. But because you (the attacking player) get priority first, they can also wait to see that you haven't pumped it, then decide not to kill it, and then you won't get another chance to pump it.

That situation can actually be further generalized. Because of the priority system, the active player gets first choice of what to do, but only the non-active player can respond to their opponent choosing to do nothing (replace active player for whoever the rules say gets priority first if the stack is non-empty).

@Zags I was suggesting something you might want to add into your own answer (which is otherwise pretty comprehensive), which is perfectly appropriate use of comments, but if you would prefer it be a separate answer, I'll post one when I have time (or someone else will first).

@Jefromi The analysis of how priority interacts with hidden information in magic is actually a fairly different analysis direction than I was taking in my answer.  I appreciate the suggestions but I think it might be extensive enough to warrant a standalone answer.

@Jefromi I had an extended discussion on the topic and added a prototype section on priority breaking an imperfect information situation.  feel free to expand on it

About the rare situation with bolt and giant growth: that sort of thing is probably much more common for those of us who play on MTGO, because there are no shortcuts there and everything relating to priority is very explicit.

For certain decks (e.g. infect), the priority issue on pumps vs. removal actually comes up fairly often.

Hey finally a good use for power sink. Two players together in multiplayer could with two power sinks counter what one could not.

@RemcoGerlich I think it also comes up frequently in paper limited Magic, but we all have the rules implications kind of ingrained in our play patterns - this is true even for players who don't know about priority rules, because they learn what you can and can't do in combat / trick / removal situations. So it's not verbalized as much, but in my experience it plays out the same as on MTGO / Arena.

Preface
While the answer by the OP is a pretty good list of examples when priority matters, the question as posed is more about "Stack vs Priority", as in, "Do the rules need the priority system when it already has the Stack?". A philosophical question warrants a philosophical answer. While such an answer is buried inside the comments, chat, and OP's answer, in my opinion it deserves its own answer.

The Stack vs the priority system
And this answer is: Yes, both the Stack and the priority system are important because they are solutions to different problems.
The rules for the Stack and for priority are so entwined with one another that it is difficult to tell them apart unless you look carefully at the rules. And carefully we shall look.

The Stack
I said the Stack and the priority system are solutions to different problems, so let's look at the problems that the Stack is trying to solve:

How do the rules handle players responding to spells and abilities? They must do that if spells and abilities that target other spells/abilities (e.g. counterspells) are to work properly. If players are to be able to respond to spells and abilities, they can neither resolve immediately nor go into a limbo when they are cast/activated/triggered.
In what order do the effects of different spells and abilities happen?

The rules for the Stack[405] solve them by saying:

When spells and abilities are cast/activated/triggered, they are put on the Stack.[405.1] The Stack is the holding area for spells and abilities waiting to resolve.
The Stack keeps track of the order in which objects are put there[405.2], and defines what happens if multiple objects are put there simultaneously[405.3].
The objects on the Stack resolve in reverse order they are put there (LIFO).[405.5]

Now, it is not difficult to see a gaping hole in this solution: it defines the order in which spells and abilities resolve given the order they are added to the Stack, but says nothing about the latter.
Moreover, there are actions that do not use the Stack [405.6]. Naturally, the rules for the Stack do not govern them. So in what order do those happen? The previous paragraph is simply a special case of this since the act of adding objects to the Stack itself does not (and cannot) use the Stack.
This is where priority comes in.

Priority
As we did with the Stack, let's begin with the problems:

When more than one player wants to be proactive (they all want to act first), who can act first?
When all players want to be reactive (they all want to act last), who must act first?

The rules for priority[116] solve them by:

Making so that, at any point in time, only at most one player can act.[116.1]
Defining who that player is at any point in time.[116.3]
Defining when spells and abilities resolve, and when steps and phases end[116.4], forcing players to act if they want to do so in response to a particular spell/ability or within a particular step/phase.

Since only at most one player can perform actions that do not use the Stack at any point in time, the order in which those actions happen is well-defined. If multiple players want to do so, those actions happen in the same order as those players' chance to act. If a single player wants to do so multiple times, that player chooses which action to perform first.

Examples
Now that we have differentiated the Stack rules and the priority rules, let's look at some examples.
Loyalty abilities
AP's Liliana, the Last Hope just resolved, emptying the Stack. NAP has a Lightning Bolt in hand.
The crux of this situation is that AP activating Lili's +1 puts a loyalty counter on Lili and puts it out of range of Bolt, but NAP casting Bolt prevents AP from activating Lili's +1. Since both actions do not use the Stack, and both players want to act first, the priority rules apply. AP can act first.
Split Second
This is essentially the same problem: a player taking an action that does not use the Stack (casting a Split Second spell) restricts what non-Stack action (casting/activating other spells/abilities) other players can take, resulting in both players wanting to act first.
Tap effect vs tap cost
AP has Wellwisher. NAP has Ballynock Trapper and wants to prevent AP from activating Wellwisher.
This is more difficult to analyze, since tapping for Wellwisher's ability does not use the Stack and Ballynock Trapper tapping Wellwisher uses the Stack.
Long story short, if AP actively wants to activate Wellwisher's ability, he can do so before NAP activate Trapper. That's priority. On the other hand, if AP wants to activate Wellwisher's ability only if NAP tries to prevent them from doing so using Trapper, then he can respond to Trapper's ability. That's the Stack.
Giant Growth vs Lightning Bolt
AP is attacking with a 1/1 with NAP at 2 life. NAP declares no blockers and it is currently in the Declare Blockers Step. Through previous events, both players know AP's only card in hand is Giant Growth and NAP's only card in hand is Lightning Bolt.
In this case, NAP has the advantage. If AP casts Growth, NAP can respond with Bolt to kill the 1/1. If AP does not cast Growth, NAP simply passes and take 1 combat damage from the 1/1.
Now, NAP's advantage does not come from their ability to respond to AP's spell because that advantage is symmetric -- AP can also respond to NAP's spell. Rather, NAP's advantage stems from NAP's ability to make their decision based on the other player's decision and AP's inability to do so. That, in turn, is due to AP receiving priority first in the Declare Blockers Step and thus having to make a decision first.
With that in mind, it does not even matter if NAP knows AP's hand. In NAP's perspective, as long as AP does not cast a pump spell, the reason why they do not is irrelevant. AP has decided to do nothing else and is bound to that decision if NAP decides the same. This is, again, by virtue of NAP receiving priority last.
To hit home the point, imagine if NAP is at 1 life instead of 2, then AP has the advantage instead. In this situation, if NAP passes, they die to combat damage. If NAP casts Lightning Bolt, AP can respond with Growth, saving the attacker. Here, AP's ability to respond prevails. The tables are turned because now the NAP wants to be proactive rather than reactive. The NAP is forced to cast Bolt regardless of AP's decision and as a result loses the advantage. On the other hand, AP now has the ability to make a decision based on NAP's decision to cast Bolt. Thus, the AP, instead of the NAP, has the advantage here.

If you'll let me know when you are done making edits,  I will help you fix the subject-verb agreements in the post.

I definitely agree that priority fills a gap that would otherwise exist in the rules; the question was really about where that gap is in game play.  I like your philosophical distinction.  However, I don't agree that your giant growth vs lightning bolt is a consequence of priority.  The two sides of your example (the 1 life vs 2 life) illustrate that it is not priority that forces a player to act first there, but rather whichever player has a greater desire to avoid the default result of the situation.

I want to note that the giant growth vs lightning bolt is a very interesting question, requiring game theory and modeling asymmetric information to fully answer, and I believe that the application of priority falls under this heading (as I tried to address in my answer) rather than it being simply a consequence of priority and the stack.  This is in large part due to there being a potentially different result that has nothing to do with priority if players have perfect information.

Yes, priority can definitely matter.
The classic example is Terry Borer's mistake involving Grave Servitude in the quarter-finals of Pro Tour Atlanta, 1996. An error which cost him the game, the match, and arguably the title of Pro Tour Player of the Year:

Borer was playing against fellow Canadian Darwin Kastle. Terry had the win in his hand. All he had to do was attack with a number of creatures. And then after blocking was assigned, he needed to play Grave Servitude from his hand on an unblocked creature (and Borer had more attackers than Kastle had blockers) and he would win. Attack. Play Grave Servitude on an unblocked creature. Win the game and the match and advance to the semi-finals.
But Borer decided to be tricky. After Kastle declared his blockers, Borer asked "Do you have any fast effects?"
The question sounds innocent enough but head judge Charlie Catino understood its importance. When Darwin said no and Terry attempted to play Grave Servitude, Catino stepped in. You see, by asking the question, Borer had passed priority. When Kastle declined to play a spell, the opportunity to play spells had passed. Borer's little tricky question made him miss his window for playing the Grave Servitude.
Surviving the attack, Kastle was able to win the game on his next turn. But wait, it gets worse. Because Borer made that mistake, he lost that game. Because he lost that game, he lost the match. Because he lost the match, he didn't advance to the semi-final round. Because he didn't advance, Borer did not get the extra pro tour points. Because he didn't get the extra points, he later lost the Pro Player of the Year race to fellow countryman Paul McCabe.
One tricky sentence cost Borer the game, the match, possibly the Pro Tour and the Pro Player of the Year title. Ouch.

Some of the terminology has since changed (we no longer use the phrase "fast effects", for one), but this would play out the same way today, due to the current versions of 116.3d and 116.4:

116.3d If a player has priority and chooses not to take any actions, that player passes. If any mana is in that player's mana pool, he or she announces what mana is there. Then the next player in turn order receives priority.
116.4. If all players pass in succession (that is, if all players pass without taking any actions in between passing), the spell or ability on top of the stack resolves or, if the stack is empty, the phase or step ends.

This is a great example and illustrates why priority is important distinct from the stack. It doesn't hurt that it shows consequences, beyond the game itself, of trying to misuse it backfiring on the offender.


text:
PDS II space cannons of third-party players
The PDS II upgrade allows your PDS units to use their Space Cannon abilities on adjacent systems (as does the Xxcha Flagship).  How does this work for third-parties involved in the combat?
For the sake of example, the L1z1x control Mecatol Rex and the Federation of Sol attacks Mecatol Rex (anyone getting deja vu?).  The Xxcha player have Space Cannon (x3) in an adjacent sector that can be applied to Mecatol Rex.  Which of the following is the Xxcha allowed to do?

Not fire their space cannons
Fire against the Sol ships (the active player)
Fire against L1z1x ships (the inactive player)
Split their space cannon dice among the Sol and L1z1x ships

The valid options are #1 (not shooting) and #2 (shooting the ships of the active player).
Shooting space cannons is optional for any player (so #1 is always an option).  Then, #2 is an option but not #3 or #4 because space cannons apply their hits to the ships of the active player, with the only exception being for the active player's space cannons.
Here are the relevant rules for Space Cannon Offense from the rules reference (my emphasis):

Beginning with the active player and proceeding clockwise, each player may use the “Space Cannon” ability of each of his units in the active system by rolling a specific number of dice for each of those units; these are called space cannon rolls.
If a player has the “Deep Space Cannon” technology, he can use the “Space Cannon” ability of his PDS units that are in systems that are adjacent to the active system. The hits are still assigned to units in the active system.
The active player must choose and destroy one of his ships in the active system for each hit result produced against his units.
If the active player is using the “Space Cannon” ability of his units, he chooses a player who has ships in the active system. That player must choose and destroy one of his ships in the active system for each hit the space cannon roll produced.

This is corroborated by the Learn to Play:

After the active player’s ships move into the active system, each player’s units in the active system may use their “Space Cannon” abilities against the active player’s ships in that system. The active player may also use his units’ “Space Cannon” abilities at this time.


text:
Hypermetabolism in Twilight Imperium
In Twilight Imperium 4th Edition, the card Hypermetabolism reads:

During the status phase, gain 2 command tokens instead of 1

You already get 2 command tokens during the status phase, and is likely a misprint.  This has been discussed on many threads, but is there an official errata from FFG?

Yes.  The living rules reference v1.1 contains the errata:

HYPER METABOLISM
The text of the “Hyper Metabolism” technology should read as follows:
“During the status phase, gain 3 command tokens instead of 2.”


text:
Who choses the targets of the Exotrireme II's ability in Twilight Imperium?
In Twilight Imperium 4th Edition, the Sardakk N'orr have a special version of the Dreadnaught called the Exotrireme.  The upgraded version of this, the Exotrireme II has the ability:

After a round of space combat, you may destroy this unit to destroy up to 2 ships in this system.

Who chooses the targets of this ability?  The Sardakk N'orr, or the player they are fighting in combat?
Note that if the Sardakk N'orr can chose the targets, this means they can sacrifice a Dreadnought (4 cost) to kill an enemy War Sun and a Flagship (12 and 8 cost respectively).

The Sardakk N'orr chooses the targets.
This thread on BoardGameGeek has an official answer from FFG on the subject:

I do have another questions about some of the "destroy abilities " in game.
Exotrireme II - sacrificial ability , Assault Cannon, Yin Flagship.
1.) Am I correct to assume that for any Destroy ability sustain damage cannot be used ?
2.) Who select unit destroyed for Exotrireme II ability? Norr player or Opponent?

Hey Fedor,
Exotrireme— 1) That is correct, sustain damage cannot be used against
abilities that ‘destroy’. 2) The N’orr player selects the units to be
destroyed.
Let me know if I can help further, –––––––––––––––––––––––––––––––––
Dane Beltrami Game Developer dbeltrami@fantasyflightgames.com

This is also consistent with the "Exotrireme" upgrade from 3rd edition, which read:

At the end of a round of Space Battle, you may destroy 1 of your Dreadnoughts present to destroy 2 present enemy ships of your choice.


text:
What Happens if I Manifest a Double-Faced Card?
If I put a double-faced card onto the battlefield with Manifest (Put it onto the battlefield face down as a 2/2 creature. Turn it face up any time for its mana cost if it’s a creature card), what happens?  Does it enter the battlefield transformed, is it a 2/2 with no abilities, or is it not even possible to be manifested?

If the answer has done a good enough job please consider accepting it.

This article explains that double-faced cards can be manifested and enter as 2/2's with no abilities.  The actual implementation of this stems from the fact that the double-faced card must already be unidentifiable in your hand and library.  As a result, you already have the card in an opaque sleeve or you have a checklist card in your deck as a placeholder, and either of these can be put on the battlefield face-down as a state distinct from transformed.
It should be noted that double-faced cards can't be turned face down if they are already a face up permanent (such as by Ixidron).  The relevant rules are the following:

711.9. If an effect allows a player to cast a double-faced card as a face-down creature spell, or if a double-faced card enters the
  battlefield face down, it will have the characteristics given to it by
  the rule or effect that caused it to be face down. That card remains
  hidden, using either a face-down checklist card or opaque sleeves. See
  rule 707, “Face-Down Spells and Permanents.”
711.9a While face down, a double-faced permanent can’t transform. If it is turned face up, it will have its front face up.
711.10. Double-faced permanents can’t be turned face down. If a spell or ability tries to turn a double-faced permanent face down, nothing
  happens.


text:
What happens in the event of a standoff in Magic?
What happens in a game of magic if neither player can win or lose?
Examples:

Both players have empty libraries and control Dragon Appeasement on an otherwise empty board.

One player controls Platinum Angel and Abyssal Persecutor and neither player has a way to remove either from the battlefield.

Both players have empty libraries and control some lands and Words of Worship on an otherwise empty board.

Both players have some lands and a copy of Beacon of Immortality, but no other way to win.

One player has an empty library, only lands on the battlefield, and only Nexus of Fate in hand, which they are using to prevent themselves from being milled.

Related, though not duplicate: https://boardgames.stackexchange.com/questions/14437/what-happens-if-both-players-have-the-ability-to-pump-their-creature-an-unlimite

Worth noting a player can still concede at any time and both players may still consider an intentional draw.

There are several variants of this situation that are quite different in the rules reasoning and outcome.  In all cases, the situation is a loop.

720.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a "loop"). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.

Case 1: players cannot win or lose the game because of mandatory abilities
The game is a draw.
Example 1: both players have empty libraries and control Dragon Appeasement on an otherwise empty board.
Example 2: one player controls Platinum Angel and Abyssal Persecutor and neither player has a way to remove either from the battlefield.
In this case, the game is a draw.  The game will eventually reduce to each player being able to do nothing but pass the turn.  This is a loop of mandatory actions.

720.4. If a loop contains only mandatory actions, the game is a draw.

Case 2: players cannot win or lose the game because of optional abilities
The game is a draw.
Example 1: both players have empty libraries and control some lands and Words of Worship on an otherwise empty board.
Example 2: both players have some lands and a copy of Beacon of Immortality, but no other way to win.
In this case, the game will eventually reduce to a loop of both players activating the ability that keeps them alive and then passing the turn.  This is a loop of optional actions that spans multiple turns.  The comprehensive rules do not cover the subject, so we need to go to the tournament rules*.  The tournament rules allow for multi-turn optional loops to be continued indefinitely and this causes the game to be a draw.  From the Tournament Rules section 4.4:

Loops may span multiple turns if a game state is not meaningfully changing. Note that drawing cards other than the ones being used to sustain the loop is a meaningful change. If two or more players are involved in maintaining a loop across turns, each player chooses a number of iterations to perform, or announces their intent to continue indefinitely. If all players choose to continue indefinitely, the game is a draw.

Case 3: only one player has an optional ability and is using it to forestall inevitably losing
The player with the optional ability loses.
Example 1: one player has Dragon Appeasement and the other has Words of Worship
Example 2: one player has an empty library, only lands on the battlefield, and only Nexus of Fate in hand, which they are using to take infinite turns where they do nothing other than cast Nexus of Fate.
This is different from case 2 because only one player is involved in maintaining the loop.  From the Tournament Rules section 4.4:

If one player is involved in maintaining the loop, they choose a number of iterations. The other players, in turn order, agree to that number or announce a lower number after which they intend to intervene. The game advances through the lowest number of iterations chosen and the player who chose that number receives priority.
...
A player may not 'opt-out' of shortcutting a loop, nor may they make irrelevant changes between iterations in an attempt to make it appear as though there is no loop. Once a loop has been shortcut, it may not be restarted until the game has changed in a relevant way. Proposing loops as an effort to use up time on the clock is Stalling.

* The Tournament Rules specify: "Information in this document may contradict (or have information not contained in) the Comprehensive Rules. In such cases, this document takes precedence."

@Allure It's a loop if player 2 isn't doing anything because you keep getting to the same game state.  "Loops may span multiple turns if a game state is not meaningfully changing."

@Allure I think I fixed it


text:
Retreating to the unrevealed rebel base
In Star Wars Rebellion, the Board Game, can the empire retreat from a battle to the system containing the unrevealed rebel base?  Assume that the battle takes place adjacent to the system containing the unrevealed rebel base, there are no imperial systems adjacent to the battle site, and there are no units or loyalty of any kind on the system on which the rebel base is hidden.  Also assume that the empire is bringing ground forces with them on this retreat.
Here is how this situation happened:

As the empire, I captured a rebel turn 1.

On turn 2, I used Homing Beacon on the captured prisoner to reveal the sector of the rebel base, Planetary Conquest to conquer a planet in the sector, and then deployed two assault carriers from the build queue to this newly conquered planet.

On turn 3, the rebels attacked me with all of the ships they had, including fighters from the rebel base (which was adjacent to where I had landed).  I still had an assault carrier left after the first round of combat and decided to retreat with it and all my ground forces (an AT-AT and two Stormtroopers).  As a result of this setup, there were no adjacent imperial systems, so I was allowed to retreat to an unoccupied system, and the system containing the rebel base had no units in it nor rebel loyalty.  The planet I picked to retreat to was the planet containing the rebel base.

Is this a valid retreat, and if so, what happens?  Does it change if the rebels versus the empire initiate the combat next to the rebel base?  Does it matter that rebel units in the combat came from the rebel base?

If the rebel player has not revealed their base before the beginning of combat, and the system it is on is unoccupied, it is a valid retreat location.  This is true regardless of which player's turn it is or whether or not units involved in the combat came from the rebel base.

Justification
The rules for retreat state:

A player must choose to retreat to a system that contains his units or
  one of his loyalty markers, if able. He cannot retreat to a system
  that contains his opponent’s units.

If there are no adjacent systems containing his units or loyalty markers, he can retreat to any adjacent system that does not contain
  units.
A player cannot retreat to a system that his opponent moved units from to initiate the combat

Meanwhile, the rules for the rebel base state:

The “Rebel Base” space is not a system.
When Imperial ground units move into the system, the base is revealed
  after all movement is completed, before resolving combat.
The Rebel player may optionally reveal his base at any time during one
  of his turns of the Command Phase

Since the rebel base is not a system, units coming from it to participate in combat do not change the situation since units must come from a system to impose a retreat restriction ("A player cannot retreat to a system that his opponent moved units from").
Also as a result of the rebel base not being a system, as long as it is unrevealed, it does not change the retreat eligibility of the system on which it is hidden.  If the rebel base is not revealed and the system on which it is hidden is unoccupied and neutral, then it is a valid retreat location for the empire (so long as there are no imperial systems adjacent to the battle).
If the empire retreats with ground forces, the base is revealed as a a result of having imperial ground forces there and a second battle will ensue.  If the empire still has some forces (such as tie fighters or other ground troops) in the first battle location, the first battle should be concluded before beginning the second rebel base battle.
If the rebels initiated the combat next to their base however, things get a little more complicated because this combat occurs during the rebels' turn.  One consequence of this is that if the empire retreats to the rebels base, the rebels will go first in the resulting combat because it is still their turn (despite the fact that the empire was the one that moved the units that initiated combat).  But more importantly, on the rebels' turn the rebels can reveal their base before initiating combat to prevent it from being a valid imperial retreat location.
Note that the July 2016 FAQ errated away the very problematic "at any time" phrasing in when the rebels could reveal their base.  It now reads:

If the Rebel player wishes to optionally reveal his base, he can only
  do so at the start of one of his turns of the Command Phase, before
  using one of his leaders.

If the rebels do not reveal their base before attacking an imperial fleet next to their base, however, the empire can still retreat to their base's system.

Aside
Before the errata to when the rebels could reveal their base, the "at any time" clause lead to a glaring timing question, with two possible interpretations:

By the point at which the empire has declared a retreat to the rebel base, it will happen; if the rebel player wants to prevent the empire from retreating to the rebel base, they must reveal the base before the empire declares their retreat.
If the empire declares a retreat to the rebel base, the rebel player can chose to reveal the base in response and invalidate the retreat.

The original rules didn't clarify on this point, but drawing on timing philosophy from other games actually leads to the same result as the errata gives us.
There are two primary philosophies for timing conflicts in games: stacks (such as in Magic the Gathering) and priority queues (like Android Netrunner).  In a stack system, a player can use an "any time" action to respond to another player's action and the responding effect happens first.  Stacks are "last in first out".  In a priority queue system, players can only have their action happen first if the rules specifically define it as superseding the other player's action (such as preventing damage in Netrunner), and otherwise it resolves after.  Queues are "first in first out", unless one thing is given preference by a specific rule.
The rules of Star Wars Rebellion give a lot of clear indicators that it is a priority queue game in terms of timing.  Every part of the game where players interact, there is a defined order for the action, the reaction, and the resolution.  Even with combat tactics cards, there is a separate step during which the recipient of damage gets to play damage block cards, meaning even one of the most classic interrupting actions (blocking damage) must be played in its specific order defined by the rules.  The conclusion of this is that option 1 (defined above) is the case; if the rebels want to prevent the empire from retreating to the rebel base, they must reveal their base before the empire decides where to retreat.  The errata supports this theory by specifying a time in the turn order when the rebels can reveal their base that is distinctly before any other actions that would be impacted by this.

Please use proper quote tags, not the coding boxes. It's extremely difficult to read when the text doesn't automatically fit into a line, and needs scrolling.

@Nij How do you do indentation in a block-quote?  I haven't found syntax that works.

A single greater-than, >, then a space, for each line in the block quote.

@Nij Thanks, but I already know how to do basic block quote syntax.  My question was whether you know how to do indentation inside a block quote.  I wanted to preserve the indentation of the rules text and only code blocks let me have the indentation I want

Why is additional indentation needed, when the blockquote both indicates separation and applies some indent as well?

@Nij Because that is the way the rulebook is formatted.  The indented subpoints are clarifications on the point above them instead of standalone rules.  This discussion belongs in a standalone meta post; not the comment section.

Then change the formatting to make it readable here. I don't know whether you're arguing from a pragmatic or an aesthetic, but either way, the codequote makes them both fail.

@Nij Stackexchange is built on collaboration.  If you have a problem with the functional choices an author has made in formatting a post, you should suggest it as an edit.  However, due to the complicated nature of the formatting in this post, I have found the syntax for including bullets in block quotes and done the edit myself.  Given this is a question about ambiguity in the rules, it is important to preserve as much of the rules being referenced as possible, including format, as that can sometimes indicate hidden meaning.