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How is a roleplaying game not a board game?
Let's say you have a roleplaying game with these elements:

a board on the table, depicting the rooms of a castle
miniature pieces on the board, representing the different characters in the game
cards and dice used as randomizers

How is this not a board game?
(The question may sound antagonistic, but I'm quite serious.  What is it that makes such a game not a board game?)

Just linking to your other very similiar question. http://rpg.stackexchange.com/questions/20149/whats-the-difference-between-a-roleplaying-game-and-a-board-game

Why is it not possible to be both a roleplaying game and a board game?  They seem to be more a continuum than an absolute.  Some things are pretty close to the middle.  Example: http://boardgamegeek.com/boardgame/127324/story-realms

To give a short, simple attempt at answer to kick things off: I would say that a roleplaying game must be partly comprised of hidden information that has been invented by one or more of the players.
That's the key difference I can see between The Arkham Horror/Mansions of Madness (boardgames) and The Call of Cthulhu (roleplaying game), where both are moderated by a Keeper.  In both setups the Keeper controls the opposition to the players, but in only one is (s)he asked to invent details, descriptions or outcomes, as opposed to just managing them.
In a boardgame, it would be seriously frowned upon for any player (even in a moderatorial role) to come up with new challenges or house rules for the others that are not in the script.  In a roleplaying game, that's practically compulsory.

Mansions of Madness has a Keeper, but Arkham Horror does not (all players are on the same side and working cooperatively). Also in Mansions of Madness, the Keeper doesn't invent any rules or plots; they just pick from a couple of predefined scenario options.

In an archetypical board game, the action focuses almost exclusively on that which can be represented by state on the board, state on a sub-board, or marker substitutions. Further, board games generally operate on the principle of "What is not explicitly permitted is forbidden."
The board itself versus the Narrative
In a Roleplaying game, the board is not the final arbiter of what is present - it's the "Gamemaster." Further, a great many RPG's do not use a map on the table at all in play; while the minis-on-map crowd has been with us from the dawn of RPG's (I was told this by Dave Arneson via email in 2005 or so, and have seen it since 1980), it wasn't the "normative method of play".
Roleplaying games, in general, operate as a radioplay - people talking about their character's actions and speaking their character's dialogue. Even when the board is present and used, it's secondary to the actions as described.
Rules Precision
Board games tend to have fairly precise, albeit often abstracted, rules. The general principle in board gaming is you can only choose actions for which the rules allow.
Roleplaying games, in general, take a different approach - what isn't explicitly forbidden is able to be attempted, and rules only delineate what's assured and what's forbidden, leaving a whole gray zone of "This can be attempted but it's up to the GM to figure out how to resolve it." Some, going back to 1975's T&T, strongly encourage "making stuff up on the fly." Including house rules to cover issues specific to your group and play style. To a lesser extent, even the 1974 edition of D&D encouraged house rules.
Some fallacies
There are several commonly held beliefs about RPG's that are fallacious. I'll address several of them in the spirit of completeness.
Hidden Information
Hidden information is neither requisite for RPG's, but strongly discouraged in a few (like Houses of the Blooded and Burning Wheel).
Likewise, it's not alien to board games. Stratego is a simple form of hidden information constructed by a player and kept from the others. More detailed forms include any board games with double blind play.
A Gamemaster/Overlord
While it's normative to have a singular Gamemaster running RPG's, several do not require one, usually sharing the duties amongst the group.
Likewise, most double-blind games require a referee, and many wargames of the 1960's and 70's presume a 3rd player will serve as referee. Not a few include the provision in the campaign rules for the GM to introduce surprises of their own.
Continuing Campaigns and Character Growth
Both of these are present in a number of board games. FGU's Star Explorer has continuing campaigns of multiple plays, and character advancement of the captain. Car Wars by SJG, Star Warriors by West End and BattleTech by FASA/WhizKids likewise allow driver/pilot experience to improve in continuing non-roleplaying campaigns.
While they are normative to RPG's, not all RPGs include them; a few are intended for one-shot play per character, and provide no means of character growth.
Speaking in Character.
It's required in Aye, Dark Master, a card game.
It's not actually required in most RPG's, the rules working just fine with the abstracted "My dude's gonna try and charm the society lady using my savoir-faire skill." It's not the norm to play in the abstracted third person, but it works.
There's a clear line
No, there isn't.
Car Wars has been straddling the line since the mid 80's... neither fully board game, in that there are suggestions on how to roleplay in Deluxe and later rulebooks, but also not fully RPG as the game is played strongly tied to the map-state.
Battlestations likewise sits just a hair on the boardgame side, but the authors themselves refuse to class it as purely either one.
Burning Empires is often described as a narrativist wargame in roleplay mode.
Diplomacy is as much a freeform roleplaying of diplomats as it is a wargame. Several of its derivatives are likewise strong on the off-map action being as important as the on-map/on-component tracking.

How is a board game not a role-playing game? Let's say you have a board game game with these elements:

an Overlord (GM) that commands the Monsters and sends Heroes on Quests..
multiple players that take on the roles of characters in the game (PC)
Timmy always screaming, "Death to the Orcs" whenever he rolls for an attack.

Board games can be role playing games and vice versa. Most board games have you take on the role of something/someone, be it a Gingerbread Man, a real estate investor, or island Settler. Traditionally, what makes a role playing game different than a regular board game are:

a campaign. Most role playing games have you play the same character over multiple gaming sessions. Most board games are played in a single sitting, where the outcome of previous games has no bearing on the current game.
variable rules. Many a GM will give a +2 circumstance bonus for clever play. GM's have been know to modify encounters from the rules to take it easier on a party of adventures that have been having bad luck with the dice, so they won't die as easily. Most traditional board games have a strict, rigid rules structure, and players are not encouraged to usually decide rules on the fly.
open objectives. Although a GM might have a particular campaign in mind, the players themselves shape the outcome of the story. Perhaps you want to go after the man who killed your father to flesh out your back story, and no amount of prodding from the GM can get you to save the village from the pending goblin horde. GM's and the players decide what the goals for their characters are.
story telling. Although I would guess many a GM, due to player interest, deemphasize the acting and "role" playing of the characters for a more hack'n'slash approach. Most board games don't have you speaking in accents, and trying to emulate conversations between Non-Player Characters.

There are of course exceptions to every difference. Some role playing games are becoming more like tactical board games. Some board games have campaigns (Descent/Risk Legacy), reward creative play outside the defined rules (Story Cubes), or have you acting out your role (Pitch). Word definitions change, so if people are calling something a board game, it probably is (at least to that person).

Definitions are only useful as long as they are useful. It is much more important that a game category reasonably describes aspects of the game that the person you are communicating with can understand, than that it can be summarized using a few technical bullets. Thus, when normal usage of a term conflicts with some suggested definition, then the definition is wrong, not the usage.
In other words, a role playing game is not a board game, because most people understand the term board game to exclude role playing games.
Of course, there is always a gray zone, where a game could realistically be described as either category.

When playing a role-playing game, you spend about 80% of your time NOT using (or referencing to) the game rules.
Try not using the rules in a board game for even a little time...

This answer does not provide any information that was not already provided.


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Goldnight Commander and Thatcher Revolt
I'm not 100% sure what happens if I have a Goldnight Commander on the battlefield and play a Thatcher Revolt. Do all three 1/1 red human tokens enter the battlefield at once, giving each of them +3/+3 (along with all creatures already on the battlefield)? Or does the first one get +3/+3, the second one +2/+2 and the last one only +1/+1?
I'm assuming the former, but it would be great if someone could confirm.

All three of your Thatchers will get +3/+3.  They do enter the battlefield simultaneously, and in the process of Thatcher Revolt resolving, Goldnight Commander will trigger three separate times.  By the time you reach the point of going to resolve each of the three Goldnight Commander triggers on the stack, Thatcher Revolt has long since finished resolving, and all your Thatchers are present on the battlefield, queueing up for their Giant Growths!

According to the comprensive rules on triggered abilities:

603.3b If multiple abilities have triggered since the last time a player received priority, each player, in APNAP order, puts triggered abilities he or she controls on the stack in any order he or she chooses. (See rule 101.4.) Then the game once again checks for and resolves state-based actions until none are performed, then abilities that triggered during this process go on the stack. This process repeats until no new state-based actions are performed and no abilities trigger. Then the appropriate player gets priority.

and:

603.6a Enters-the-battlefield abilities trigger when a permanent enters the battlefield. These are written, "When [this object] enters the battlefield, ..." or "Whenever a [type] enters the battlefield, ..." Each time an event puts one or more permanents onto the battlefield, all permanents on the battlefield (including the newcomers) are checked for any enters-the-battlefield triggers that match the event.

This means that when the tokens come into play at the same time, each individual trigger from Goldnight Commander goes on the stack one after another, and you resolve one at a time. Each one will give all your creatures +1/+1.
To sum up, all the tokens will get +3/+3! Remember, the triggered abilities go on the stack after Thatcher Revolt finishes resolving, at which point you already have all the tokens in play!

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Can I flicker Aurelia to get more than two attack phases?

Whenever Aurelia, the Warleader attacks for the first time each turn, untap all creatures you control. After this phase, there is an additional combat phase.

If I attack with Aurelia once, then flicker her (e.g. with Acrobatic Maneuver), will her second attack also count as "attacks for the first time each turn," thereby allowing me a third?

You'll need another way to blink her - Restoration Angel doesn't work on Angels.

Yes.
There are two completely separate Aurelia, the Warleader in the scenario.
The first attacked in the first Combat Phase before being removed from the battlefield using Acrobatic Maneuver.
The second was placed on the battlefield by the blinking ability and went on to attack in the second Combat Phase.
It's of no relevance that the same physical card represents both Angels.

400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. [...]

When a card refers to itself by name, it means "this object".

201.4. Text that refers to the object it’s on by name means just that particular object and not any other objects with that name, regardless of any name changes caused by game effects.

As such, the post-blinking Angel first attacks in the second Combat Phase, triggering the creation of a third.

+1 especially for the note that this doesn't work with Restoration Angel! It's amazing how many people forget that clause.  Also, note that the fact that Aurelia untaps all creatures (and not just those that attacked) means it's theoretically possible to go infinite with e.g. a Breeding Pool and a couple of Arbor Elves.

@StevenStadnicki My favorite Aurelia trick is to use her to untap Izzet Staticaster

[mtg:Cloudshift]

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What can I do to make my opponent play faster at Regular REL?
I play low-key Magic the Gathering tournaments, like release parties and Friday Night Magic. They're good fun but I'm often stuck looking at the clock, trying to avoid a game-3 draw. I know the problem isn't me because my sets against quick-playing opponents are usually over with 20 minutes to spare.
The obvious non-procedural workarounds are:

Draft fast aggro
Try really hard to win 2-0 so you don't need to play a third game

I don't exactly have the skills to do this consistently. :)
At higher rules enforcement levels, you can call a judge if your opponent is taking too long. That option's not readily available at Regular REL, though, and generally you're supposed to be forgiving of a player's inexperience or procedural missteps. Bearing that in mind, what can I do to encourage other players to play faster without being a jerk?

I'm surprised that you seem to think there is no possibility of official intervention at Regular REL.  From a recently updated official document on Judging at Regular REL:

General Unwanted Behaviours -

There will sometimes be issues that do not have official fixes, but
  need to be discouraged. These include, but are not limited to;

Players taking unreasonable amounts of time side-boarding or making
  play decisions
Inadequate shuffling after a search
Asking for, or
  providing, strategy advice during a tournament match or booster draft

In all of these cases, educate the player on better behaviour – for
  example, alternate shuffling techniques or the importance of allowing
  players to make their own decisions. Players continuing to exhibit
  specific unwanted behaviour after being instructed otherwise should be
  issued with a Game Loss.

A Judge should be available to advise persistent time-wasters that, actually, there is a limit to how long they can spend "thinking about their moves" in a game of Magic.  Obviously the Judge will be gentle at first, as this is only Regular REL; but really, no one is being done any favours , if new players are not told early on that they need to play the game at  reasonable pace, that is to say, fast enough that a full three games can be comfortably completed in the time allowed.
Don't be a jerk about calling a Judge over, but equally, you shouldn't be afraid of doing so. It's not being rude to ask, in a neutral and polite way, for the basic ground rules of tournament Magic to be enforced.

Being courteous to new and/or inexperienced players is important, especially in more casual settings.  Offer to answer (or find a third party to answer) any questions they may have if that's the holdup.  It is understandable to be indecisive about a crucial play, but it is also their responsibility to be courteous to you and not stall out the game (whether they intend to or not).

You're close to addressing the intent of my question, but I'd like some more specifics. Like, for instance, when someone's taking a lot of time to ponder an almost-identical board state for several turns straight, what are some behaviors I can adopt to courteously encourage faster play?

@Alex P - Its hard to get into the specifics because everyone will take things differently and it depends on how courteous you want to be.  Usually a simple "Are you done?" will let them know that they need to commit to something.  Other times you might have to get a bit more pushy.  At some point, they are doing you a discourtesy by continuing to take time doing nothing.


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Can an opponent folding make you go from probable winner to probable loser?
I was watching a World Series of Poker video, and noticed a strange thing with the percentages that each player had for their chance to win the hand.
Before the flop, after all but 3 players had folded, the percentages were like this:
Player A: 9♥9♣ - 35%
Player B: A♦Q♦ - 40%
Player C: J♥10♦ - 25%
Player C folded, and immediately player A went to 56%, while player B went to 44%. Player B was the favorite based on his cards, but after player C folded, player A became the favorite. How is this possible?
Here is the video in question, at the relevant timestamp:
https://www.youtube.com/watch?v=oZP3OrtcO-Q&feature=youtu.be&t=1m22s

Shouldn't this be asked on/migrated to Poker SE?

Alice has $35, Bob has $40 and Carol has $25. Carol dies and leaves $21 to Alice in her will and $4 to Bob.  Before Carol's death, Bob was the richest of the three of them, but after her death, now Alice is the richest.  How is this possible? Now -- how is the "puzzle" I have presented any different from the situation you have presented?  I do not see why you think this is an impossible situation; can you explain why you believe it is impossible?

Note that these percentages take into account the removal from the possible community cards of all cards which were known to be in the hands of players who had already folded. This is what accounts for the resulting percentages being somewhat different than an analysis would show when only considering the cards shown.

@Glorfindel We do get poker questions here all the time; I'm not sure what the criteria is for which site is better.

@EricLippert That's a pretty good analogy. What I was missing in the first place was that the cards that would have originally helped player C win  would be better for player A than player B.

Very simplified, consider only 1 pair hands (which are most likely, thus primary contributor): With A, B & C: B wins if an A or Q shows (6 cards). C wins if a J or T shows (6 cards) and B does not win (not 6 cards). A wins if both B & C don't win (not 12 cards). With only A & B: B wins if an A or Q shows (6 cards). A wins if B doesn't win (not 6 cards). Largest difference is that A no longer looses when a J or T shows up. Thus, most of the combinations where C would have won are now won by A. The increase for B is boards where B would have made a pair, but C would have made more than a pair.

Seconding the suggestion for moving this to Poker SE. Having questions repeated here which are either already answered there, or would be answered faster and better by that community, is nonsensical.

This question is on topic for this site, (and Poker).  Sites within the SE network are allowed to have coverage areas that overlap.  We don't need to overrule the questioner by moving the question.

@patludwig an asker who is active on just four SE sites and with accounts on less than a dozen? Which is more likely - they knew of both Poker and BCG, or they didn't know Poker exists and asked here because it was the closest thing they had? There's no "overruling", there's just movement from an okay-ish place to an extremely good place.

@Nij - I don't know how much clearer I can be. This question is both welcome and on topic here.  If you wish to discuss further, please take it to meta.

@Makyen I don't know about that, talking WSoP, the percentages are calculated by those who already know what each player has in hand, and thus knows what cards are in deck pre-flop to calculate percentages on.

Suppose the five community cards wind up being 9♦, 10♥, 10♣, J♠, and 3♠. Then C would win with a better full house than A, but A's full house is better than B's pair of 10's. Before C folds, this would count towards his 25% win chance; after he folds it counts for A's 56%. When C folds, we're essentially taking his 25% chance to win, and splitting it up between the two remaining players. The issue then becomes that the cards that help C out also help A more than they help B, so most of C's 25% goes to A rather than B after C folds.

Ah, I must've thought the Jack was another 9 when I came up with the hand.  I'll fix the example.

Example is spot on, but you could do more about explaining why A enjoys a greater gain from C's fold than B. While B is favored 40% before the fold, that still means he loses to 60% of the possible community card permutations.

A much more extreme, but simplified sample.  A is winning 60%, B is 0, C is 40%.  B is 0 because every combination that B wins, A will win even more.  Now A folds.  All of this 60% went to B, so be now becomes 60% to win, and C stays at 40%.

@Nelson is such a hand possible; that every possible card which would help player B actually gives A then win?

Never mind, I guess with enough card eliminated from options by being in other players' hands it is. B has KK , and A has AA of the same 2 suits as B. At least 3 other players already folded KKQQQQ.

While I don't have the exact math to prove it, it certainly seems reasonable.  The question to ask is, in the 25% of cases where C would've won, who would've had the second best hand?  If the answer is almost always A, then you'll get the results you saw.
Here the thing that really boosts A's chance are having a 9 on the table.  But when C is in play, that also leads to a lot of straight possibilities that would give the hand to C.  With C out of the picture, those hands strongly favor A.
Note that B's chances to win have NOT gone down.  They've actually increased from 40% to 44%.  It is just that now all the remaining hands go to a single player, so the comparison looks different.  B was always more likely to lose than win. He was just the individual most likely to win.

It's almost the Spoiler effect in action.

When player C folded, both player's chances went up. B's chances rose from 40% to 44%, while A's chances rose from 35% to 56%.
What happened was that A captured "most" of C's chances. The reason is that both players would benefit from a 9 that would make a straight for A, and a "set" or full house for C.
B benefited from capturing C's chances of making a second pair behind his "set" (or pair) (not a lot). Meanwhile, A benefited more from C's chances of getting the 9.
So B is no "less" probable a winner when C folded, but s/he went from first of three to second of two in terms of "relative" probability.

B did not go from a probable winner to a probable looser
The odds went up (slightly)
Your odds would never go down as a result of a fold
The odds were
Player A: 9♥9♣ - 31%
Player B: A♦Q♦ - 43%
Player C: J♥10♦ - 26%
After C folded
Player A: 9♥9♣ - 56%
Player B: A♦Q♦ - 44%
Consider the 99
As a pair it is currently ahead
But any of 4 cards will beat it - AQJT
There are also straight and flush draws
After the fold the 99 is still ahead
But now now only 2 cards will beat it AQ  (and flush and straight)
AQ only went up slightly as it still has to improve to win
If AQ improves to like a pair then JT would need 2 pair or a set and that is just not likely
It was the correct for B to call even though he was behind.  He was getting correct pot odds to call.
Jarvis was down to 23 big blinds so he felt like it was time to make move. If he could fold one player out and only facing two overs then a good play. If he cannot fold a player out or facing an over pair then a bad play.  That is poker.
I watched the hand again. When B only called you could put him on AQ or lower. AA, KK, JJ, TT, and AK would have raised (against Duhamal a chip leader playing a lot of pots).  A was counting on folding out B and C not having a monster.  As is turned out C was raising light.  When it got to B he should mathematically  call unless he is facing AA or QQ and that is not likely.  The right mathematical call.

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Commander damage from Mimic Vat token?
I've exiled my commander using Mimic Vat. Do the tokens it creates from it deal commander damage?

No. The Commander rules state (CR903.3) state: "[Being a commander] is not a characteristic of the object represented by the card; rather, it is an attribute of the card itself. The card retains this designation even when it changes zones." and drives the point home with the last example: "A permanent that's copying a commander (such as a Body Double, for example, copying a commander in a player's graveyard) is not a commander."

No, it is an at attribute of the card itself, not a characteristic that is copyable. From the Mtg Comprehensive Rules:

903.3. Each deck has a legendary creature card designated as its commander. This designation is not a characteristic of the object represented by the card; rather, it is an attribute of the card itself. The card retains this designation even when it changes zones.
Example: A commander that's been turned face down (due to Ixidron's effect, for example) is still a commander. A commander that's copying another card (due to Cytoshape's effect, for example) is still a commander. A permanent that's copying a commander (such as a Body Double, for example, copying a commander in a player's graveyard) is not a commander.

A cards characteristics are:

109.3. An object's characteristics are name, mana cost, color, color indicator, card type, subtype, supertype, expansion symbol, rules text, abilities, power, toughness, loyalty, hand modifier, and life modifier. Objects can have some or all of these characteristics. Any other information about an object isn't a characteristic. For example, characteristics don't include whether a permanent is tapped, a spell's target, an object's owner or controller, what an Aura enchants, and so on.


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Can I target an indestructible creature with a 'destroy target creature' spell?
Of course the spell won't resolve, but is the indestructible creature a legal target for a spell with the effect "destroy target creature"?
For example, can I target Gideon, Champion of Justice, animated by its second ability, with Rapid Hybridization?

Yes, Indestructible creatures are legal targets for spells/abilities that say "destroy target creature."
The spell actually does resolve, but when it attempts to destroy the creature rule 700.4 prevents it from happening. The requirements for a "legal target" for a spell must be a permanent, unless the spell/ability specifies otherwise. Indestructibility does not modify the rules for targeting, unlike the rules for protection (702.15b A permanent or player with protection can’t be targeted by spells with the stated quality and can’t be targeted by abilities from a source with the stated quality).
You can target Gideon with Rapid Hybridization, and when it resolves it will fail to destroy Gideon and will create 3/3 frog owned by Gideon's controller.

114.2. Only permanents are legal targets for spells and abilities, unless a spell or ability (a) specifies that it can target an object in another zone or a player, (b) targets an object that can’t exist on the battlefield, such as a spell or ability, or (c) targets a zone.

700.4. If a permanent is indestructible, rules and effects can’t destroy it. (See rule 701.6, “Destroy.”) Such permanents are not destroyed by lethal damage, and they ignore the lethal-damage state-based action (see rule 704.5g). Rules or effects may cause an indestructible permanent to be sacrificed, put into a graveyard, or exiled.

Thank you! As far as I can see, it's a nice trick to have a 3/3 creature for 1 at instance speed :)

And note that if, while it's on the stack, another effect is added that removes indestructibility, then the creature will be destroyed.

You can target anything that matches the description given for what's a legal target (unless Shroud, Hexproof or similar prevents you). Rapid Hybridization has you pick a target creature. Since Gideon, Champion of Justice is a creature (at this time), you can pick it as the target.

But Gideon is indestructible (at this time). It can't be destroyed [CR 700.4], but Rapid Hybridization instructs you to destroy it. Can't trumps do [CR 101.2], so you're asked to do something impossible.

609.3. If an effect attempts to do something impossible, it does only as much as possible.

So in this case, the following happens:

Destroy target creature. It can't be regenerated. That creature's controller puts a 3/3 green Frog Lizard creature token onto the battlefield.

Gideon's controller will get to keep Gideon, and he will gain a Frog Lizard.

Unless it says "destroy target creature that's not indestructible" than yes, you can target it.
And yes, the spell will resolve.  Gideon won't be destroyed, but his controller will still get his Frog Lizard
The same goes for spells that cannot be countered and tapping and untapping creatures.`

this is from the ruling section from the gatherer link for 'Rapid Hybridization'

If Rapid Hybridization resolves and the creature isn’t destroyed
  (perhaps because it’s indestructible), its controller will still get
  the Frog Lizard token.

That only answers half the question since the creature could have become indestructible after it was targeted.


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Gods dying and the legends rule
So this came up in a game I was playing today. I had an Athreos, God of Passage with enough devotion that it was a creature, and I cast another (it makes sense, I swear). I chose to sacrifice the newcomer.
This will trigger the remaining Athreos and I will return the dead god to my hand unless my opponent pays three, correct? Athreos was a creature when it died, and remained so after because its type-setting ability only applies on the battlefield.

Yes, the ability of the God that remains on the battlefield will trigger. When you play the second copy of Athreos, you will control 2 of them. Then, when state based effects are checked, by rule 704.5k, you have to choose one to keep and move the other to the graveyard. This triggers the ability of the one still on the battlefield.

Technically, the other Athreos is just moved to the graveyard, not sacrificed, and so (for example) Savra, Queen of the Golgari won't trigger.

Rule 704.5k says, the duplicate is put into the owner's graveyard.  Is that the same as dying?  ...  I guess it is from rule 700.4, which says "The term dies means “is put into a graveyard from the battlefield.”"

Yes. It would die. It is not sacrificed, but the Athreos does die.


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Do face-down creatures with death trigger activate normally?
If a face-down creature has a "When this dies [...]" effect (i.e. because of Ixidron), will that effect activate when it dies?

Done. That should clear up any timing issues.

Ixidron doesn't give anything a "When this dies ..." ability...

I'm voting to close this as unclear because it's not clear whether the creature's death trigger is (a) on its front face or (b) granted to it by something else, and that's significant.

Short answer: Yes, if it had one, but the creature lost that ability when it was turned face-down.

"When this dies" is a leaves-the-battlefield ability [603.6c], and leaves-the-battlefield abilities trigger based on their existence, and the appearance of objects, prior to the event rather than afterward [603.3d].
So it doesn't matter what abilities the creature would have if it was face-up or will have in the graveyard; all that matters is what ability it actually does have. Only leaves-the-battlefield abilities the face-down creature has just prior to dying will trigger when it dies. Normally, that wouldn't be any, but some cards (such as Cauldron Haze) could grant them some.

It will not, if that ability was granted from some rules text on the card. It will if something else is granting it that ability after Ixidron turned it face-down (Cauldron of Souls).from the CR:

707.2a If a face-up permanent is turned face down by a spell or ability, it becomes a 2/2 face-down creature with no text, no name, no subtypes, no expansion symbol, and no mana cost. These values are the copiable values of that object’s characteristics.

There are no turn-based actions that instruct you to turn a creature face up when they go to the graveyard.

110.6. A permanent's status is its physical state. There are four status categories, each of which has two possible values: tapped/untapped, flipped/unflipped, face up/face down, and phased in/phased out. Each permanent always has one of these values for each of these categories.

110.6c A permanent retains its status until a spell, ability, or turn-based action changes it, even if that status is not relevant to it.

What concerns me is the timing minutiae: isn't the card considered face-up by the time it gets to the graveyard, thus restoring the effect?

"110.6d. Only permanents have status. Cards not on the battlefield do not." Which to me means a card going in the graveyard loses its face down status (otherwise cards with Unearth and other such things would lose it from Ixidron, and I'm fairly sure they do not).

@Circeus, It doesn't lose its face-down status. It's a brand new object with no memory of its past self.

@Circeus, I'd have to check but this could well be another case of the very common "last known information" rule, where things happen based on the state of play at the moment a card left its zone, rather than the card's new condition...

@Circeus, it surely does lose its face-down status, in the same way that object ceasing to exist lose their status. But, it doesn't gain a face-up status. This means that it has no text (707.2a), and that continues to remain true until an ability, spell, etc. tells you otherwise (110.6c)

@Circeus I doesn't matter that it is face up in the graveyard. Rule 603.6d tell us to look for the object as it was in the battlefield for leaves-the-battlefield abilities. Note that abilities that trigger when something is "put into a graveyard from anywhere" are not considered leaves-the-battlefield abilities. Therefore, a face down progenitus would be shuffled.


text:
How does Void Winnower affect face down spells and creatures?
Void Winnower says

Your opponents can't cast spells with even converted mana costs. (Zero is even)

Your opponents can't block with creatures with even converted mana costs.

If I control a Void Winnower, does it prevent my opponent from casting Morph and Megamorph cards as face down spells? Does it prevent face down creatures from blocking?

I assume you meant to ask about blocking, not attacking.

Yes, that's what I meant. I fixed the question.

I cant find Void Winnower in the Card Database is it banned?

It's from the new set. I asked this in anticipation of the release.

I see I must get this card... it has blue black control written alllll over it haha

Void Winnower does prevent your opponent from casting face down spells and blocking with face down creatures.
The most important rule here is 202.3a:

The converted mana cost of an object with no mana cost is 0.

The description of Morph is in rule 702.36a:

Morph is a static ability that functions in any zone from which you could play the card it’s on, and the morph effect works any time the card is face down. “Morph [cost]” means “You may cast this card as a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost by paying {3} rather than paying its mana cost.” (See rule 707, “Face-Down Spells and Permanents.”)

Since the spell has no mana cost, you cannot cast it for its mana cost, so you need an alternative mana cost to cast it [CR 117.6a]. In this case, the rule allows you to cast it for an alternative mana cost of {3}, but that does not change the actual mana cost of the spell.
And the description of Manifest in 701.31a says

To manifest a card, turn it face down. It becomes a 2/2 face-down creature card with no text, no name, no subtypes, and no mana cost. Put that card onto the battlefield face down. That permanent is a manifested permanent as long as it remains face down. The effect defining its characteristics works while the card is face down and ends when it’s turned face up.

In addition, rule 707.2a says

If a face-up permanent is turned face down by a spell or ability, it becomes a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost. A permanent that enters the battlefield face down that wasn’t cast as a face-down spell also has these characteristics. These values are the copiable values of that object’s characteristics.

Putting these together, we can see that face down morph spells, and any creature that is face down for any reason has no mana cost, so Void Winnower prevents your opponent from casting face down spells and blocking with face down creatures.

Void Winnower's Gatherer page now has a ruling that says

The converted mana cost of a face-down creature spell or a face-down creature is 0. Void Winnower will stop face-down creature spells from being cast and face-down creatures from blocking.

Void Winnower works:

Face down spells: "Exception from the rule".
Face down creatures:  "This kind of creatures Like "manifest" or "tokens" are not affected by the card".

Author note: I am a player from South America -Chile. I started MTG 16 years ago with the portal deck and today im still an active player. I hope this post help you with your seeking.

I'm not 100% clear what you're trying to say, but it definitely sounds like you're saying that face down spells and face down creatures aren't affected by Void Winnower, but the existing answer pretty clearly explains why they are, and the ruling it quotes from Gatherer clearly demonstrates that it's right. (Also... tokens aren't face down.)

In response to your comment-as-answer (which should eventually get moved here by a mod)... no worries about your English, it's certainly better than my Spanish. The main point I was trying to make is that there isn't an exception from the rule: face down spells and cards have CMC zero so they are affected. Or do you mean that the fact that they have CMC zero is the exception?


text:
What happens if the legend rule doesn't apply to only one of a pair of legendary creatures with the same name?
Brothers Yamazaki has the ability

If there are exactly two permanents named Brothers Yamazaki on the battlefield, the "legend rule" doesn't apply to them.

So, say I control two Brothers Yamazaki (and there are no others on the battlefield), a Grizzly Bears, and a Leyline of Singularity, and I have a Spy Kit attached to one of the Brothers.
Spy Kit has the ruling

The set of names the equipped creature has includes the names of all nonlegendary creature cards in the Oracle card reference, including the back faces of double-faced cards. Notably, the equipped creature won’t gain the names of tokens, such as Zombie, Goblin, and similar. It also won’t gain the names of noncreature cards that have become creatures, such as a Wandering Fumarole that has become a creature.

So, the overall result here is that I have 3 legendary creatures:

One named "Brothers Yamazaki"
One named "Grizzly Bears"
One with many names, including both "Brothers Yamazaki" and "Grizzly Bears"

Then because of the ability on Brothers Yamazaki, the "legend rule" applies to creature number 2, but not to creature number 3. What exactly does that mean? What happens to creature number 2?

I think you may have found a rules hole! :D

#mtgrules favored choosing one, though can't provide much credence. Looking for other avenues.

I also asked them, and their answer is what I refer to in my comment on the currently accepted answer.

Yeah, going to see what comes of just Tweeting this at Wizards_Magic, Gavin Verhey, and Matt Tabak.

All of the creatures survive.
This question has finally been definitively answered by the Dominaria United Commander card Cadric, Soul Kindler, which directly creates the situation in question on its own. It has the following abilities:

The “legend rule” doesn’t apply to tokens you control.
Whenever another nontoken legendary permanent enters the battlefield under your control, you may pay {1}. If you do, create a token that’s a copy of it. That token gains haste. Sacrifice it at the beginning of the next end step.

Resolving the second ability creates a legendary token with the same name as a legendary permanent you control. The legend rule doesn't apply to the token, but it does apply to the non-token permanent. The set's release notes document contains the following ruling for Cadric

If, while you control Cadric, Soul Kindler, you also control a token legendary permanent and a single nontoken legendary permanent with the same name, the legend rule will not cause you to put either one into your graveyard.

Finally, a properly official answer! This ruling implies that the correct way to interpret the legend rule is that: When assessing the game state for the legend rule, you should pretend that (permanents to which the legend rule doesn't apply) don't even exist.
Slight shame that the rules still don't make this unambiguous, but at least there's a proper source now.

Note that the rules were actually reworded to address this, although I'm not 100% convinced they don't have the same potential question. Still, rulings!

Independent of how you arrived at this position, you now get to choose between the Brothers Yamazaki that has the Spy Kit attached and the Grizzly Bears. The premise of the question is wrong; the legendary rule still applies to each Brothers Yamazaki in play. However, it does not apply to a grouping of exactly two Brothers Yamazaki.
The specific exception created by the rules texts of the Brothers Yamazaki allows a pair of legendary creatures named Brothers Yamazaki to exist on the battlefield, directly contradicting rule 704.5K. Refer to the Magic the Gathering Golden Rules:

101.1. Whenever a card’s text directly contradicts these rules, the card takes precedence. The card overrides only the rule that applies to that specific situation. The only exception is that a player can concede the game at any time (see rule 104.3a).
704.5k If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”

The card text of Brothers Yamazaki only prevents the legend rule from triggering when the game sees two of them existing. Look back at the rules text:

If there are exactly two permanents named Brothers Yamazaki on the battlefield, the "legend rule" doesn't apply to them.

The special condition created by the rules text applies specifically to the pair of them.  It does not stop the Legendary rule from seeing the two Legendary "Grizzly Bears." Since two creatures named "Grizzly Bears" that are legendary exist under your control, you must choose one of them and sacrifice the other. Further, the interaction of two Brothers Yamazaki, Leyline of Singularity, and Spy Kit will affect every other creature you control.
Twitter?
The persistence of this rules hole drove me to Twitter for answers, with a direct Tweet to Wizards_Magic, Gavin Verhey, and Matt Tabak.

Rule Hole challenge: @GavinVerhey @tabakrules @wizards_magic - Brothers Yamazaki+Spy Kit+Leyline of Singularity - drunkcynic

This prompted a response from Matt Tabuk:

@drunkcynic @GavinVerhey @wizards_magic Nothing happens. You continue to control all three permanents. - tabakrules

Which confused me, so I sought to get some clarity:

@TabakRules @GavinVerhey @wizards_magic Clarity: W/ LeylineOfSingularity, will Spy Kit'ed 1/2 Brothers Yamazaki 704.5k non-legend creatures? - drunkcynic

Initially, I thought my hopes were dashed:

@drunkcynic @GavinVerhey @wizards_magic Two Yam Bros. means ignore those perms and look at everything else to see if legend rule applies. - tabakrules

Yet, all was not lost:

@drunkcynic @GavinVerhey @wizards_magic Spy Kit has u lose creatures until the legend rule doesn't apply, likely by offing the eq. creature. - tabakrules

That, and I think Gavin Verhey was hungry:

Mmmmm, Yam Bros. Delicious! #wotcstaff - gavinverhey

Disclaimer:
Resorted to pinging these two only because there was a shortage of other avenues. Ask Wizards has been defunct for a while, and there wasn't a clear answer from the existing rules or sources.
Deeper Analysis
Doesn't Apply - There are two instances in Gatherer for the rules text, "doesn't apply:" Mirror Gallery, released in Betrayers of Kamigawa, and Brothers Yamazaki, released in Champions of Kamigawa. Each affect the application of the Legend Rule. Mirror Gallery sweeps broadly in its contradiction of the rule, removing it from the game entirely. The Borthers Yamizaki narrow that restriction down considerably, only stopping it from applying to two of them.
Them/They/Those - Their are 793 occurrences in Gatherer of cards that include "They," "Those," or "Them" in their rule text. Each apply to a grouping of objects, be it creatures targets, cards being considered, or other effects, where something is affecting them jointly or you are choosing a portion of them. The rules texts of cards are, for the most part, rather exact; the "They," "Those," or "Them" is intentional, just as the times where further rules text is used to narrow the application of effects to a portion of the group. As an example, consider Tamyo, Field Researcher. Her first ability states:

+1: Choose up to two target creatures. Until your next turn, whenever either of those creatures deals combat damage, you draw a card.
Here, the ability establishes a grouping of two creatures, with a result if either member of the group satisfies the condition.

Narrowing the scope of the search further, consider just cards with the rule text "each of them." Here, the cards create a group, and then apply an effect to each member of that group. In contrast, Brothers Yamazaki ability establishes a group, consisting of exactly 2 Brothers Yamazaki, applies an effect to the group. The legendary rule applies to each Brothers Yamazaki individually, and to a group of three or more Brothers Yamazaki. Refer back to the earlier citation of Rule 101.1; the ability of Brothers Yamazaki only contradicts the legendary rule 704.5k for the group consisting of exactly two Brothers Yamazaki. it does not conradict the rule for each of them, just them.
Yes, Magic the Gathering uses Them, Those, and They to address a group objects affected by an event. The event will then either work with the entire group, or affect portions of the group, using modifiers like: Each, the Rest, from Among, etc. There is a certain refined legalese in how the rules texts of Magic the Gathering cards is constructed, based on the grammar and structure of the English language. "to them" occurs three times in the entire card pool; Brothers Yamazaki, Silence the Believers, and Gauntlets of Chaos. In each, the effect creates a group, and then the group is affected. In every card where an effect creates a group, and affects a member of the group, the rules text explicitly does so. Since the rules text for Brothers Yamazaki doesn't say "each of them" or "either of them," it doesn't affect the two individually, just the group.
A notable factoid.
Champions of Kamigawa brought the first change to the legendary rule. Prior to Champions of Kamigawa, the first player to get a legendary object in play "won", turning each other copy of that card in the game into a dead draw. With Champions of Kamigawa, follow on copies of the card would reset the condition instead, causing all copies in play to be sacrificed. This mattered in part because of the numerous "Legendary" cards in Kamigawa.
It was with Magic 2014 that we got the rule as it stands today, where 705.4K looks at each players battlefield independently. While each player can control copies of the same legendary object, one player can't control two copies without effects that specifically allow him to do so. However, there is also a unique interaction between Brothers Yamazaki and the Legendary Rule as it stands, looking at the Oracle ruling (specifically noting the date, coinciding with Magic 2014 release):

7/1/2013   If a third Brothers Yamazaki enters the battlefield, the legend rule will apply. If one player controls more than one Brothers Yamazaki at that time, that player will have choose one and put the rest into his or her graveyard.

While the current Legendary rule only cares about your battlefield, Brothers Yamazaki still looks at the entire battlefield. Baring any additional effects, there can only be two Brothers Yamazaki in play at once. When a third comes into play, the player with more than one follows the actions of 704.5K.

Your  argument ignores that the Brothers ability extends to the whole permanent, which is also named grizzly bears.

@Hackworth No. The ability merely changes how the legend rule is applied.  Instead of it requiring X >=2, where X is the number of legendary objects sharing the same name, applying the legend rule to the Brothers Yamazaki needs X>=3. This is only for the pair of Legendary Brothers Yamazaki; neither is individually protected.

That is a very free interpretation of the brothers' ability and not consistent with the Mirror Gallery ruling.

I disagree with your statement that "them" doesn't apply to the "Grizzly Bear" part of the object named "Brothers Yamazaki". "Them" refers to two objects named "Brothers Yamazaki", and doesn't partially exclude different components of those objects.

@Samthere You misunderstand. Them applies to the pair of objects named Brothers Yamakazi. It did not apply to either object individually.

@DrunkCynic I see what you mean as a pair, but Magic uses "they, them, those creatures" to refer to previously mentioned objects, not to check that they still meet the condition. e.g. Surprise Deployment says "return that creature to your hand". It doesn't matter if the object stopped being a creature - a Theros God will still return to your hand if you don't have devotion. The Brothers say "if you have a pair of objects of a certain quality, the Legend rule doesn't apply to those objects". Not "the Legend rule doesn't apply to those objects if looked at together, but does with other things".

@Samthere No. The Brothers say that the legend rule doesn't apply to that pair of objects. There is a programmatic distinction between the pair of objects and those two objects.

@DrunkCynic I understand your logic in terms of parsing the English, but it's not how Magic uses it. Look at Guardian Beast. It uses the word "them" to apply to a group of objects. By the logic you use here, the protection would only stop someone gaining control of all of them as a group, not of any one of them. I'm aware we've put a lot of discussion into comments at this point so I'll back off, but I don't think this will be resolved without official input.

@Samthere Quite possibly, though I'm comfortable being in the minority opinion. It is regrettable there isn't a JeremyECrawford for clear MtG rulings. The key component to this argument is 101.1, explaining the limitation by using "them" instead of "each of them."

You say in your answer "Magic the Gathering uses Them, Those, and They to address a group [of] objects affected by an event", and much of your argument is based on the precise interpretation of the wording. Can you provide a single example of a card or interaction in which interpreting those words the way your answer does leads to the correct conclusion and interpreting them as other answers do leads to the incorrect conclusion? Without such an example, your premise that those words have the specific meanings that you ascribe in a way that is relevant to card functionality is merely conjecture

The Magic rules do not uniquely determine what happens here.
The text of Brothers Yamazaki is vague and none of it, its rulings, nor the rules explain the wording "does not apply". Both of the other answers are consistent with the Magic rules, but they do not follow from them. Using common sense, I think either interpretation is reasonable.

Are you saying that you think the "this" in "this is called the 'legend rule'" does not necessarily mean the entire rule 704.5k? That's a kind of surprising interpretation to me, given that 704.5k is literally a rule.

@Jefromi I mean that the word "apply" is vague and not defined in the context of the game.

I don't think there's really any possible meaning of "apply" besides "take the rule, and do what it says to the things it says to do them to", or any possible meaning of "this rule" besides, well, the rule that it's within  (704.5k). The rules aren't required to define every English word that appears in them or on cards; we're expected to read and understand at some point.

I think this is probably the most accurate answer. We might lean towards assuming everything survives, because the Legend Rule can't "see" the real Brothers, but that's not clearly specified. It's possible that the rule still applies to the Bear, and that the rule can "see" the Brothers but not remove them, which could mean that the Bear has to die.

I asked actual judges, and this seems to be the current most accurate answer. Acceptance of this answer is hopefully temporary, and will change if and when there is an official ruling and/or the relevant rules change to make this situation unambiguous.

As it stands, there are three answers of note, covering each result: nothing is sacrificed, the Grizzly Bears are sacrificed, and you choose to sacrifice the Grizzly Bears or the Brothers Yamazaki equipped with the Spy Kit. Recommend editing out "both of", and detailing the cases.

My reading would be that nothing happens. The legend rule is:

704.5k If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”

It seems like there's no way to apply this without having two or more creatures to apply it to.
That is, this whole rule is the legend rule, not just the consequences. If the legend rule doesn't apply to a creature, then the "if...two or more" doesn't involve that creature.
So to apply the legend rule in this case, we look at all the creatures it's allowed to apply to, and discover just one. So there aren't two or more legendary creatures with the same name (as far as the legend rule is concerned) and nothing happens.

One could alternatively read "the legend rule doesn't apply to them" as the legend rule doesn't do anything to them - in other words, the "apply" part is the ("choose this creature to keep" or "put this creature in its owner's graveyard"). Though on second thought that seems a bit less likely.

Yeah, I think there's really no choice but to think of the decision about whether to apply the rule in terms of the whole rule. The whole thing is the legend rule, including the "if...", not just the consequences.

You get to keep all 3 creatures.
The legend rule reads:

704.5j If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”

The Brothers' ability makes the legend rule not apply to them as long as there are exactly 2 of them on the battlefield. What "not applying" means can be derived from the rulings for Mirror Gallery or Sakashima of a Thousand Faces:

Mirror Gallery removes the “Legend rule” while it’s on the battlefield.[..]

While the “legend rule” doesn’t apply to permanents you control, you can control any number of legendary permanents with the same name and none of them will be put into the graveyard.

While Mirror Gallery is on the battlefield, the game is played as though the legend rule did not exist, or, put differently, the legend rule check is disabled for all permanents.
Accordingly, while exactly two Brothers Yamazaki are on the battlefield, the legend rule is not checked for either of them. Any legend rule check that would compare either of the Brothers Yamazaki to any other permanent for name identity is not performed at all. That means the Grizzly Bears is also safe from the legend rule, because the one check that could get them killed (with the Spy Kit'ed Brothers) is not performed.
Therefore, it does not matter whether or not either of the Brothers shares a name with Grizzly Bears or yet other permanents. As far as the legend rule is concerned, the two Brothers do not exist on the battlefield at all.

There is a discreet difference between two creatures in the battlefield being able to break the rules of Magic the Gathering and another card that removes a rule.

Not sure what you mean by that. Mirror Gallery removes the legend rule, Brothers remove the legend rule as far as Brothers are concerned.

Brothers does not remove the Legend Rule, it just shifts the number of which are required to trigger the rule.

@DrunkCynic The card literally says that the legend rule does not apply - that is, for the purposes of those two objects, the legend rule does not exist.

The main uncertainty/ambiguity of this question that I don't think is resolved by the referenced rulings is whether "The legend rule doesn't apply to [a set of permanents]" means "Legend rule checks involving those permanents are skipped" (as you suggest) or "Legend rule checks between those permanents are skipped". Since the referenced cards both disable the legend rule for all permanents you control, that difference doesn't matter functionally for those cards.

The Grizzly Bear dies.
The Legend Rule states:

704.5k If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into
  their owners’ graveyards. This is called the “legend rule.”

The Grizzly Bear is Legendary thanks to Leyline of Singularity. But why do I believe it gets snuffed? Let's look at the Spykit:

Equipped creature gets +1/+1 and has all names of nonlegendary
  creature cards in addition to its name.

I've placed emphasis on the part that I feel is relevant. The name of the Brother isn't changed to "Abattoir Ghoul Abbey Gargoyles ... Brothers .. Grizzly Bear ... Zebra Zombie", it gets ALL the names individually. Compare this with Angelic Armaments; The equipped creature, if it's a Grizzly Bear, now has the colors Green and White. Not Green-white, but Green and White separately. Anything affecting Green affects this equipped Grizzly, as would anything affecting White.
Now, applying the Legend Rule:

There is only one "Abattoir Ghoul" on the battlefield, so no problem
"Abbey Gargoyles" is also alone
...
There are two Brothers Yamazaki, but there is an effect in play that supersedes the Legends Rule in this case. No effect.
There are two Grizzly Bears in the field. The Legend Rule applies to the Vanilla Grizzly because it does not have an ability that lifts it and it is placed in the graveyard.

What you appear to be missing about the last two points is that you're talking about the same permanent. Brothers Yamazaki's ability excludes the entire permanent from the Legend rule, not just the creature type. Therefore, no matter what happens, the pair of Yamaziki Brothers will be safe from that rule, independent of it's other creature types.

@TheThirdMan You're right, but I'm not convinced that protection applies tothe Grizzly. Will rephrase soon.

The rules text doesn't protect a Brothers Tamales from the Legendary rule, it protects "them" from the rule.

@DrunkCynic That's exactly what my answer describes, and that's why the Grizzly gets snuffed.

tl;dr– It's ambiguous, with up to 6 possible interpretations of the rules.  However, regardless of the interpretation, the controlling-player can keep all of their permanents.

Background: What's the problem?
I think most folks imagine the Legend-Rule as:

If multiple Legendary permanents that are controlled by the same player have the same name, then all but 1 must be put into their respective owners' graveyards.  The player that controls them may select which remains.

Then the Legend-Rule applies to a plurality of permanents, making it tricky to assess what it'd mean if an overriding rule specifies that the Legend-Rule can't apply to a partial-subset of them.
However, that's not what the official rules actually say.  Instead:

704.5j If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”
—"Comprehensive Rules" for Magic: The Gathering [PDF]

So the Legend-Rule actually applies to players, not permeants.
However, that's clearly not how the text on Brothers Yamazaki,

If there are exactly two permanents named Brothers Yamazaki on the battlefield, the "legend rule" doesn't apply to them.

, is meant to be understood.  Instead, it seems pretty clear that the text means that the Legend-Rule somehow fails to interact with the two Brothers Yamazaki.
I'd agree with @KSFT's answer that the exact mode by which there's a failure-to-interact is ambiguous.

Three interaction-points.
The Legend-Rule's text somehow references Legendary-permanents in three places:

Counting them.

If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards.

Allowing them to be chosen.

If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards.

Having them put into their owners' graveyards.

If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards.

So if the Legend-Rule doesn't apply, then we know that at least 1 of these doesn't apply.
Additionally, we can note that in the simple case of just 2 Brothers Yamazaki, neither is put into the graveyard.  This means either Interaction (1) or/and (3) must not-apply.

Consequences of the possible interpretations.
So we know that:

Interaction (1) or/and (3) don't apply.

Interaction (2) may or may not not-apply.

Possible scenarios:

Interactionsthat don't apply
Interactionsthat apply
Consequences

1, 2, 3

Brothers Yamazaki isn't counted, so Legend-Rule never triggers.

1, 3
2
Brothers Yamazaki isn't counted, so Legend-Rule never triggers.

1, 2
3
Brothers Yamazaki isn't counted, so Legend-Rule never triggers.

1
2, 3
Brothers Yamazaki isn't counted, so Legend-Rule never triggers.

2, 3
1
Legend-Rule triggers; player must choose to save Grizzly Bears as it's their only option.  Brothers Yamazaki not put into graveyard due to non-interaction.

3
1, 2
Legend-Rule triggers; player presumably would choose to save Grizzly Bears since Brothers Yamazaki is immune.  Brothers Yamazaki not put into graveyard due to non-interaction.

When Interaction (1) doesn't apply, then the Legend-Rule doesn't count one of the Brothers Yamazaki, so there's only 1 Legendary-Grizzly Bears.  Nothing happens.
Whenever Interaction (1) does apply, Interaction (3) must not-apply.  And if Interaction (3) doesn't apply, then the player can choose to save the Grizzly Bears, as the Brothers Yamazaki are immune to going into the graveyard anyway.
In short, the controlling-player doesn't have to put anything into the graveyard regardless of interpretation.

Summary: The controlling-player doesn't have to remove anything.
The Legend-Rule interacts with Legendary permanents in three ways:

counts them;

allows them to be selected;

puts them into the graveyard;

and we know that at least 1 of these doesn't apply, and that (2) can't not-apply by itself.
Regardless of interpretation, the controlling-player can keep all of their permanents, because:

Interaction (1) doesn't apply, so the Legend-Rule never triggers.

Interaction (3) doesn't apply, so the controlling-player can choose the Grizzly Bears to be saved, then the Brothers Yamazaki is protected anyway.

The one niche interpretation would be arguing that Interactions (1) and (2) do apply, but (3) doesn't.  Then, the controlling-player would have the option (but not requirement) to put the Grizzly Bears into their owner's graveyard.

Comments are not for extended discussion; this conversation has been moved to chat.

Upkeep step - Set up and situation:
You have these creatures:

One named "Brothers Yamazaki"
One named "Grizzly Bears"
One with many names, including both "Brothers Yamazaki" and "Grizzly Bears"

The legendary rule says:

704.5j If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”
—"Comprehensive Rules" for Magic: The Gathering [PDF]

And the text on 'Brothers Yamazaki' says:

If there are exactly two permanents named Brothers Yamazaki on the battlefield, the "legend rule" doesn't apply to them.

Main Phase - How the rules apply:
So, as soon as state-based effects are checked and the rules applied simultaneously.  The rule '704.5j' has a condition 'If a player controls two or more legendary permanents with the same name', so we still check that as it applies to the player, so we can list all of those duplicately named permanents:

Two legendary permanents with the name(s) "Brothers Yamazaki" (but one also named  "Grizzly Bear")
Two legendary permanents with the name(s) "Grizzly Bear" (but one also named "Brothers Yamazaki")

Now we have checked the condition, we see if we can try to apply the rule (that player chooses one of them, and the rest are put into their owners’ graveyards) to either pair of permanents:

Grizzly Bear ✔ (can be chosen, can be put in graveyard)
Grizzly Bear (née Brothers Yamazaki) ❌ (can't be chosen, can't be put in graveyard)

and

Brothers Yamazaki ❌ (can't be chosen, can't be put in graveyard)
Brothers Yamazaki ❌ (can't be chosen, can't be put in graveyard)

This is because of the exceptions for when:

There's exactly two permanents named "Brothers Yamazaki".

Which means we make sure that 'the "legend rule" doesn't apply to them.' (i.e. those permanents found by looking at their names). And this means not only are the two "Brothers Yamazaki" exempt, the second of the two Grizzly Bears is also exempt from the legendary rule (i.e. the parts that say you chose 'one of them').
That because that Grizzly bear (née Brothers Yamazaki) is one of *exactly two permanents named "Brothers Yamazaki" that cannot have the legendary rule applied to it.
Now we follow the remaining parts of the rule, having picked the Grizzly Bear with no other names:

and the rest [of the named permanents] are put into their owners’ graveyards.

I've added in square brackets, my interpretations of which permanents the 'rest' part means.
Ultimately, it looks like when told to pick one of the two Grizzly Bears, we have to pick the one without the rules text 'the "legend rule" doesn't apply', and then when told to put the rest into their owner's graveyard (which is still part of the legend rule' we don't put that card (i.e. the one with the rules text 'the "legend rule" doesn't apply') into the graveyard.
Now, there is an issue:

704.3. [...] If any state-based actions are performed as a result of a check, the check is repeated; [...]

So we still have our two pairs of legendary creatures with identical names, and a state-based action was performed (although it had no result, the checking was still performed.) we have to repeat the check, seemingly ad infinitum. However...

704.7. If multiple state-based actions would have the same result at the same time, a single replacement effect will replace all of them.

We can replace these infinite checks with a single replacement effect ( that does nothing ), and continue until next time priority would change.
End Step - Too Long; Didn't Read:
You get to keep all three permanents, and dodge an infinite loop in the process. Congrats!

Clean up Step -  Addendum:
Q: But when checking the pair of Grizzlies, you can't count the one that is also named 'Brothers Yamazaki' because the rules text on that card only applies to 'permanents named Brothers Yamazaki'.
A: Well yes, but that card doesn't lose its name:

201.2a Two or more objects have the same name if they have at least one name in common, even if one or more of those objects have additional names. An object with no name doesn’t have the same name as any other object, including another object with no name.

One of the two Grizzly Bears has additional names, and still gets the benefits from the rules text stating "the "legend rule" doesn't apply to them."

Perhaps there's another interpretation: Since the Leyline of Singularity has made all permanents legendary, the Spy Kit does nothing (except add +1/+1). There are no non-legendary creatures to gain names from.

This is incorrect. Spy Kit adds the names of all nonlegendary creatures based on the Oracle reference.

Re-read Spy Kit. It adds the names of every non-legendary creature card to the equipped creature; every creature card ever printed.

@KSFT Yes, but Leyline of Singularity makes all permanents (not all permanents in play, but all permanents) legendary.

@Xerxes Cards not in play aren't permanents. Rule 110.1

Incorrect - Spy kit does not care about what has gained the legendary supertype as part of the game, it applies all the names based on the oracle type and text of all cards that exist in magic the gathering. The type granting ability does not interact with leyline.

It's also worth noting that magic has a layer system, so even if spy kit and leyline could interact the way you suggest, they wouldn't. Spy kit adds names in layer three (the text layer) and leyline of singularity works in layer 4 (the type layer). This means that Spy Kit adds all names of nonlegendary permanents BEFORE leyline of singularity has made everything legendary.


text:
How do I find out a fair price for my Magic the Gathering cards?
Back in the day, I would check Scrye magazine to figure out how much my Magic cards should sell for, but they folded two years ago. Where's a good place to price my collection these days?

are you looking to sell the whole collection?  Just a few cards?  Or are you just curious as to the relative worth of the cards?  Also, how old are the cards?  Are they an old collection from the 90's, some of the more recent sets?  Or a decent mix?

@Pat Looking to value a collection of 90's cards, most likely for sale.

If you want to know what you can actually sell individual cards for, I think you can't do better than ebay. If you look at price indices like Scrye used to have, you run into the problem that what a shop can sell a card for is typically much higher than what you, a private individual, can achieve.
Bear in mind as well that prices for individual cards are much higher than buying in bulk. In other words, you might work out that your collection is worth thousands of dollars, if you were to sell each rare individually. But if you tried to sell the same thing to a shop, or in a single lot on ebay, it would sell for only a small fraction of this.
The only other caveat is if you have many extremely rare old cards from the first days of Magic. In this case, the wear and tear of the card has a very large impact on the potential price. Again, ebay will give you an excellent guide to how much these can vary (try doing a search for "Black Lotus" for example).

Another great and reliable source is http://sales.starcitygames.com/spoiler/spoiler.php which has a nice search engine and rather stable prices.
Just reduce the prices by something like 20 or 30% to account for the money they want to make on the cards. The important thing is the relative value of the cards.

well, Bobby. They do need to make a profit on their sales... So you probably get 20-30% less selling to them than they do selling to you, and that's the same 20-30% you'd not get selling directly to consumers. That's the way things work in all used goods markets.

magiccards.info has a very nice price chart that compares prices at various conditions across many online retailers for every card. It's also 1000x more useful than Gatherer for searching for and browsing through Magic cards.

While you can search for only 10 cards at a time, the Apathy House Trade Evaluator is a nice way to find reasonable prices.
When I've traded in the past, others have requested I use Apathy House to value my cards, and when I've sold on eBay, the prices I have received have been close to what Apathy House suggests.

Another concept is magiccardmarket.eu (also known as magickartenmarkt.de in Germany), which is a user-to-user trading site. Anyone can sell their cards at a self-defined price, which has the interesting side effect that you can see what cards actually sell for very well. It features both private and professional sellers, and will indicate the difference.
To give a quick example, let's assume I wanted to find out a "fair" price for Vigor, I could look on its product page on magiccardmarket to see the following information (this is for the Lorwyn printing):

You can see a number of prices, which I'll explain due to the lack of official documentation on the site:

From gives you the cheapest price of availability of this card, with at least Excellent condition
Foils from does the same, only counting Foils
Price Trend is a fictional number, calculated from recent average selling prices per day
the graph on the right illustrates recent prices and also shows the Price Trend, which is helpful to see recent developments - this will also let you gauge whether you can trust the previous figures

Now, all of these values need to be taken with a grain of salt, as so far, this includes all sellers registered on the site. Most of the time, the cheapest card prices will be from Spain or Italy (as they are in this case), which of course is fine if you're from those countries, but might mean that if you'll mail-order them, you'll have to pay more shipping or even toll costs than is reflected in the price numbers here.
In addition, different regions may affect how valueable a certain language will be. Japanese cards, for example, sell exceptionally well in Europe, even among people not familiar with the language.

Now, depending on what you would consider a "fair" price, your method of determining it may vary, but here's a method I use when looking for a value I can use for buying or trading:

select the card and printing (edition) of the card you want to gauge through the search function
set the condition, language and other applicable values through the filters

if you're a registered member, you'll also get the option to only show sellers from your country. If you're not, you'll have to take a little more effort, but nothing will be "hidden"

look at the result list for prices, keeping in mind that some entries may stray from the average (or have comments further explaining in what ways this card differs from what you would expect) and may need to be discarded in the interest of a truly representative result

Following this method, you should have a good idea of how this card is being traded, and apply your individual judgement of fairness to it. For example, I would go about it like this...

The cheapest seller from my country happens to sell their Near-Mint Lorwyn Vigor for €8,98, which is fairly true to the price average. The next closest prices scale pretty much linear upwards to the highest price - €14,90.
  Looking at the selling prices, the card hasn't been often sold for more than €10,00 and since that seems to be a price slightly above the Price Trend (a rising figure, as of right now), selling it for that amount or a little more may be a good idea.

This appears to be a better method for me that searching on ebay, considering you might also find the self-drawn Vigor playmat, Amulet of Vigor because it's close enough of a search result, or in general don't have to mess around with a whole lot of other stuff due to the system being designed specifically for card trading, along with having no idea where that price comes from, and whether it's justified.

Most people, and stores, that I know use reputable online sellers or mass resellers to price their cards. In the case of my LGS, here in Canada, that's Face to Face Games. For US prices, Star City Games is pretty popular, and as a mass reseller indexing site, I see TCGPlayer used a lot for pricing. For Euro pricing I believe CardMarket is a popular one. A more recent site, newer perhaps than many of the other answers is Scryfall, which uses some aggregate data from TCGPlayer and CardMarket to show prices for each different version of the card on the results page.

You are not going to get list price for your cards, no store buys at scg prices. If you want a reasonable indication of what price your cards will fetch you should look at the buylist prices of major retailers, that is what you are going to get for your cards. The list price is for trading not buying.
Scg is a decent buying partner, they are always very fair with there grading and if you have cards they want they give reasonable prices. They also have a very attractive 50% trade bonus if you want to trade up instead of just selling cards for cash.

You're assuming he intends to sell to a store, he may be looking for pricing to put on ebay, for private sale or for trade values.


text:
Does 'fight' involve combat?
The text for Ulvenwald Tracker says:

{1}{G}, {T} : Target creature you control fights another target creature. (Each deals damage equal to its power to the other.)

Does this have anything to do with combat? Or is it just direct damage between two creatures? For example, can one of the creatures have defender? Or what if one of them is tapped?
I've been assuming it is more like the damage dealt by a Prodigal Pyromancer.
Also: are the two creatures then “tapped” until their next untap step? ie: could you use Ulenvald Tracker to make two creatures fight in your pre-combat step, then enter the combat phase with a creature who just “fought” untapped? Could you make two creatures fight who are both tapped?

The entirety of the ability is summarized in the italicized text: each creature deals damage equal to its power to the other. There are no special restrictions on "fight" beyond the normal rules for targeting and abilities on the stack (Ulvenwald Tracker can't make your Ravager of the Fells fight an opponent's Geist of Saint Traft, for instance, because the Tracker can't target a hexproof creature).
If one of those creatures isn't around when the ability resolves, no fighting will occur.
Here are the full comp rules for 'fight':

701.10. Fight
701.10a A spell or ability may instruct a creature to fight another creature or it may instruct two creatures to fight each other. Each of
those creatures deals damage equal to its power to the other creature.
701.10b If a creature instructed to fight is no longer on the battlefield or is no longer a creature, no damage is dealt. If a
creature is an illegal target for a resolving spell or ability that
instructs it to fight, no damage is dealt.
701.10c If a creature fights itself, it deals damage equal to its power to itself twice.
701.10d The damage dealt when a creature fights isn't combat damage.

Here's some minutiae about how this relates to other rules:

Abilities that only affect the assignment of combat damage, like
first strike and trample, don't do anything.
Lifelink, deathtouch, and infect/wither do still apply, since they modify all
damage that a permanent deals.
Damage can still be prevented or
redirected normally, just like damage from a Lightning Bolt.
In the case of protection, a creature with protection from the source
setting up the fight can't be targeted by it; a creature with
protection from the other creature but not the fight effect (e.g. if
you use Ulvenwald Tracker to make a red creature fight a creature
with protection from red) can still be made to fight, but protection
will prevent the damage it receives.
Note how the rules I quoted don't say anything about tapped or untapped creatures. Tapped creatures can fight just fine. Fighting will not cause an untapped creature to become tapped.

Just verifying, regenerate can be used as well when making two creatures fight?

@Damainman Short answer is yes. Regeneration doesn't care about the source of the damage, or combat damage vs. non-combat damage.

Regeneration doesn't strictly care about damage at all, for example it also handles death by Doomblade and other non-damage based sources.

"The entirety of the ability is summarized in the italicized text". I disagree with this sentence, there are many details that the reminder text - which, like all reminder texts, is in my opinion hateful and wastes a lot of space on the cards, making them less beautiful to look at ... - is not able to provide , and which should be specified elsewhere.

What Fight does is described within the italicized reminder text. It has nothing to do with combat, defender doesn't matter because you are not declaring attackers, it doesn't care about those creatures tapped status.

(Nitpickery: Fight isn't defined by the reminder text, it's formally defined by the comprehensive rules entry for fighting, as outlined in Alex's answer.  To use magic parlance, it's essentially a keyword and not an ability word; it has an 'official' definition.)

@Steven, specifically, Fight is a "keyword action". (CR 701 for keyword actions in general, 701.10 for Fight)


text:
How can I get rid of indestructible creatures with a Red and White deck?
I am creating a Red-White commander deck using Gisela as my commander.  I noticed that my deck is incredibly weak against a deck with any sort of indestructible creature.  I know of the board sweeper Terminus, but I was wondering if red/white has any other tricks up its sleeve to get rid of tricky creatures.  I'm looking for both sweepers and target-specific cards.

Rolling back the title. This isn't our canon question on removing indestructible creatures as it and its answers are - and always have been - focused on red and white. Changing the title doesn't change that, nor is it appropriate as it's significantly changing the meaning of the question. If there is to be a canon question about removing indestructible creatures for any and all colours, that needs to be asked in a new question. This question does convey typically helpful information, but that information can just resurface in the canon question.

@doppelgreener Agreed - the edited title didn't even match the body of the question, let alone the original intent or the answers. If the idea was to turn it into a generic question, it wasn't even a good attempt at it.

There are a variety of general answers for indestructible permanents:

Exile effects, which are your real bread-and-butter for all kinds of removal.
Toughness-reducing effects against creatures.
Sacrifice effects.
"Tuck" (move to library) effects.
Bouncing permanents (temporary).
Stealing permanents: the indestructible thing isn't a problem if you control it, right?
Ability- and action- restricting cards like Pithing Needle and Pacifism, if all you're worried about is disabling a card rather than removing it from the battlefield.

White is probably the strongest color for dealing with indestructible permanents after they've resolved. Some of your options are:

Oblivion Ring and similar enchantments provide single-shot answers to any non-land permanent. Note, in particular, Grasp of Fate as the multiplayer-oriented variant.
Path to Exile and Swords to Plowshares are low-cost instant answers for creatures.
Return to Dust for is a nice two-for-one against artifacts and enchantments.
Final Judgement, Descend Upon the Sinful, and False Prophet are an exile-based sweeper.
Hallowed Burial and Terminus are "tuck"-based sweepers.
Condemn can "tuck" a troublesome creature, although only when it's attacking.
Pacifism effects may be good enough if you're just trying to get rid of a blocker or prevent a card from using its activated abilities; Faith's Fetters and Prison Term are probably the best choice there.
Angel of the Dire Hour can wipe out a wave of indestructible attackers.
Elesh Norn will clear out a lot of weenies even if they're indestructible.
Evangelize and a lot mana: steal all their stuff.
Gideon, Champion of Justice will exile everything else on the battlefield.
Oblation "tucks" any nonland permanent at the cost of giving your opponent more cards.

In red:

Chaos Warp can "tuck" anything.
Into the Core can answer indestructible artifacts like Darksteel Forge.
Apocalypse and Decree of Annihilation are exile-based sweepers.
Warp World and similar cards will remove the offending permanents, at the cost of giving your opponent new toys to replace them.
Insurrection will let you take all of an opponent's creatures for a turn — usually that's enough to finish off a player or feed them all to a sacrifice outlet like Ashnod's Altar so you don't have to give them back.

Colorless cards worth noting:

Duplicant is a popular card for exiling creatures.
Brittle Effigy, Amulet of Unmaking, and Helvault provide targeted exile effects, though not very cost-effectively compared to what you can get in white.
Karn Liberated and Ugin, the Spirit Dragon can easily exile multiple troublesome permanents.
All Is Dust is a sacrifice-based sweeper.

Don't forget Faith's Fetters in there with Pacifism! :)

Excellent list! Oblation is another one I'd include, with similar power and utility to Chaos Warp.

Apocalypse , Path to Exile, Swords to Plowshares, Crib Swap, Parallax Wave, Archon of Justice, Witch Hunter, Evangelize, Helm of Possession, Preacher, Tariff, Warp World, ...
The most effective answer is to learn to use the Gatherers Advanced Search to search for keywords in the rules sacrifice, exile, gain control, then exclude cards that are not red, white, or colorless*. You will get some false positives, but it is a start.
Like so: Color=NOT(B|U|G) AND Text=Exile+Target+Creature
Like so: Color=NOT(B|U|G) AND Text=Sacrifices+Target+Creature
Like so: Color=NOT(B|U|G) AND Text="Gain Control of Target Creature"

@shujaa, I actually added the searches. I thought I did it originally, but was having issues with creating multiple (OR x,y,z) AND (OR a,b,c). It might be the case that Gatherer doesn't support that sort of search/syntax (or I just suck)

Although toughness reduction is not particularly white or red (which does gets +/- effects, though), you could look at creatures with Wither or Infect. In control-stealing, red has many temporary stealing spells and effects with stuff like Act of Treason, Blind with Anger, Grab the Reins, Mark of Mutiny, Threaten, Tibalt, Traitorous Blood, Zealous Conscripts... White has the non-time limited Preacher, though.

The answers here were all correct at the time, but there have been new cards printed that I believe are worth adding. Three newer cards specifically remove the ability indestructible, they are:

Burn from Within
Hour of Devastation
Bonds of Mortality

The first two are playable in your Boros deck, the third being green is not, but all three specifically remove indestructible.


text:
What is an efficient way to organize my magic collection?
Currently, I have a rare binder with all of my rares, and the rest of my cards are broken into several boxes by color, gold/multi color, and land.  The problem with this methodology is that if I have a specific card in mind that's a common, I have to search through the entire box until I find it.  Is there a better way to manage by cards?

Be a Party Girl and use The Dewey Decimal System.

There are a lot of ways to organize your cards that are efficient. What it is going to come down to, is what sort of efficiency are you looking for.
Deck building efficiency - This is pretty much a non-issue if you use digital deck builders, but if you don't know exactly what cards you own, it is helpful in finding possible alternatives for cards you want to run but don't own. Because all cards are near other cards of the same color/type, it is easier to find cards to fill out your deck.

Color, Card Type, Mana Cost, Alphabetical

Card finding efficiency - This reduces the size of all your box divisions, making it easier to find a particular card.

Set, Alphabetical (or collector number)

Trade/Deck Idea efficiency - Separating the Rarest cards from the most common cards allows you to easily find more valuable cards, or cards that an entire deck can be built around.

Rarest/Non-rare, any other sorting criteria.

Size efficiency- With many of the other sorting types, you may try to separate the individual Colors/Sets by placing them in their own box and filling up empty space with deckboxes or basic lands. When you organize for space, you need to only separate sections with index cards cut to fit card sleeves.

I first pull out the valuable cards to go into my binder. Then I organize the rest by Block -> Set -> Alphabetical. In addition to this, I use a collection manager of some sort (currently Essential Magic, but there are plenty of options) so I don't have to go digging through the actual cards when I work on deck building.

For me I have a box for:
1. Black
2. Blue
3. Green
4. Red
5. White
6. Uncommons
7. Artifacts
8. Lands
Creatures are separated from non creatures.
Sorted alphabetically by set.
Somewhat slimmed down by eliminating cards there are 10 or more of through most of the collection. For good cards like lightning bolt, swords to plowshares, etc. I don't limit at 10.

I find "by set" irrelevant. If I need a disenchant, I don't want to look through every set.
Color -> alpha by first letter
I don't mind flipping through all the white Ds to find something and it's easy to sort. Some letters get bun.ched together based on how many cards UVWXYZ for example in most colors.
If I want to search, I search using Oracle. I have a decent idea of what I own.

I've stopped playing, but I used Color -> Creature/Non-Creature -> Alphabetical, not sorting by expansion.  When I was playing all cards were equally available for deck-building; if the newer blocks/sets don't work that way then you'd want to sort by that first.  I found the creature/non-creature split to help manage the volume while planning and assembling decks.  (I don't know if this is typical -- I was never an excellent player -- but I tended to think about deck-building as having those two, related, sub-tasks.  So I'd choose creatures, choose spells that complement that, perhaps adjust creatures, etc.)

I found the best way to sort my cards was by:

Color
Creature / Non-Creature
Converted Mana Cost.

After you sort it is this way you can easily compare the effectiveness of each card and you will be able reduce the size of your usable cards.

Put value cards in a binder. I put all my land in a seperate box. Another box is then organized into columns based off of color/artifact/multicolor. Those columns are organized by format, then into set in chronological order as they were released. Each section is in alphabetical order. The columns for Standard contain dividers based off of how close they are to rotation as well as what set. If a card is a staple like lightning bolt, I have it in a box that was for a fat pack that is organized into a similar way. If a card has been printed multiple times, I put them all with the most recent printing of the card. I try to get rid of any copies over what I think I will need generally 8 since I card pool with someone.

I think the easiest way to sort and find cards is by Block->Serie->Color, and if you're hardcore, in alphabetical order.
This setup is good both for searching for a specific card you know about, vague searches like "blue cantrip" and for casual browsing.

I’m thinking of breaking up my commons and uncommons into 10 boxes, as follows (all the rares being in binders):

Box 1- Core sets: grouped by creature/non-creature/non-basic land,
ordered alphabetically.  Anything that I find that’s been printed in
a core set would go in here (whether that print is from a core set)
Box 2 – Latest block: grouped by creature/non-creature/non-basic
land, ordered alphabetically.  At this particular time this would be
all my Innistrad cards
Box 3 – Second latest block: grouped by
creature/non-creature/non-basic land, ordered alphabetically.  At
this particular time this would be the Scars of Mirrodin block.
Box 4 – White cards: grouped by creature/non-creature, ordered
alphabetically.
Box 5 – Blue cards: grouped by creature/non-creature, ordered
alphabetically.
Box 6 – Black cards: grouped by creature/non-creature, ordered
alphabetically.
Box 7 – Red cards: grouped by creature/non-creature, ordered
alphabetically.
Box 8 – Green cards: grouped by creature/non-creature, ordered
alphabetically.
Box 9 – Artifacts, Multi-color, colorless, non-basic land: grouped by
creature/non-creature, ordered alphabetically
Box 10 – Basic lands

With this setup, I’ll always have my standard cards easy to find (hence grouping the core sets).  Once a block cycles out of standard it’ll get distributed into boxes 4-9 (unless a card is put into the core set, then it goes into box 1).
The most strenuous part of this would be picking out anything in a core set, but that doesn’t have to all happen at the same time, they can migrate into the core set box over time.
I'm going to try this and I'll update to let everyone know how this turns out.

I also use the Block->Set->Color->Alphabetical organization method.  I can usually lay my hands on a card I want in a couple of minutes once I know that I want it.
I don't try to optimize for "find a good cheap red creature", I can use Gatherer for that sort of searching and then go find it in my collection (since I also have the containing sets information on the Gatherer page).

I have my collection primarily sorted by set. I like this method because it optimizes for the "find a given card" case. If I want a Platinum Angel, for instance, I only need to search my cards from Mirrodin, M10, M11, and M12. The worst case would be searching for something like a Llanowar Elf, while the best case would be searching for, say, Emrakul.
Within a given set, I may divide by rarity, color, and type. But sorting by set is best balance of findability and re-sortability that I have come up with.

Although I'm new to the game and still trying to find a good way to sort the 3K+ card collection my brother just gave me I personally believe the best way to sort cards for a specific card would be alphabetical with index cards to separate the letters. That method is only good when you have a lot of time on your hands depending on the collection size since if you just bought your first toolkit it would be easier to start with those than with boxes upon boxes. This is just something I know my friends and their parents do and it seems to work very well 90% of the time in case they misplace the card when it goes back. And if you are trying to make decks such as maybe a low mana cost deck with all one mana creatures you could do a mana sort deck where the prices go up in each section and in the individual sections you can separate by color, rarity, rotation, alphabetical, or how often you think you'll use it. These our just a few thoughts i have after looking threw the ways friends sort their cards and how I'll be sorting my cards.

+1 Alphabetical with index cards is an expandable system because, as your collection grows, you can move from {A, B, ... , Z} to {Aa, At, Be, Br, ... , Za}. Very nice to have a solution that can be as granular as the size of your collection requires.

First I have current standard in separate boxes. They are separated by block then color then alphabetical order. After rotation commons and uncommons get separated by color then alphabetical order in penny sleeves in groups of 4 (playsets). If I have more then 2 playsets of a given card from the same set.. it gets trashed or given away. I do all my deck building on gatherer this makes it easy to find anything in my collection.  All rares go into binders by color and alphabetical order. Standard rares in a separate binders by block and color.

bro buys thousands of cards and shoves the pricey cards in his binders and dumps the rest on the floor.
I have tried by set and block and such, but it was to hard to keep adding sets with each new release. The easiest way i found was to sort by rarity. Multi-row boxes for each rarity. Then i seperate each by color. white, blue, black, red, green, gold, dual, artifact and land. Then each is sub sorted by the first letter of its name. So when bro needs a white common card that starts with s. I have a 4 inch stack of cards to finger through to find it in a few seconds and never have to keep making and adding dividers and reordering for new sets. If you don't want extra bulk. The cheap penny sleeves can hold 8 or so singles. So i put cards with 6 copies in the sleeve so when i get another copy i can set it aside in a bulk box to trade into shops. A lot of shops offer deals for extra bulk. Bring in a few hundred and they give you around a penny piece and will swap you a free pack or something. This way the bulk is kept way down and super easy to find cards bro needs. If i had some of the better cards. I would consider doing decks cause it would be easy enough to look up the types of cards i need for a type of deck and then pull out the ones i have and see what i could toss together.