When are pieces worth more (or less) than their nominal value? Which are the most common situations in which pieces are worth more/less than their value, in point?

For example, I know that a protected Knight on 6th rank (3rd for Black) of columns d and e may be worth at least as much as a Rook (thus 5 points). The same for a very strong fianchettoed Bishop.  Another example: a Rook on 7th rank (2nd for Black) usually is worth a Pawn more than its normal value, while 2 Rooks there may be worth 3 Pawns more than their normal combined value (if opponent's King stays on 8th or 1st row respectively, of course).

Are there other similar situations?
While I don't think it's reasonable to list every noteworthy situation, here are a few more that will probably be good general guidelines.  You can use rules-of-thumb like this in order to evaluate material imbalances in your own games:


the bishop pair may be worth a rook and two pawns
the bishop pair and a pawn is worth a knight and a rook
a knight on the 6th rank is worth a rook if it cannot be traded off or chased away (and it is close to the action)
an unopposed dark square bishop is worth a rook if the opponent has played g6 and the queens are on the board
a rook on the 7th is worth an extra pawn
doubled rooks on the 7th is usually good for at least a draw
the queen may be worth two rooks if the side with the queen can start an attack.
three minor pieces may be worth a queen - take this with a large grain of salt, in every position, one side or the other usually has a decisive advantage so each case must be carefully considered
a minor piece, a rook, and a pawn are sometimes worth a queen
however, the queen with a pawn is usually stronger than two knights and a rook (for some reason, the knights just don't coordinate well, I've never had this situation in my own games)
three pawns are worth more than a piece in the endgame but much less than a piece in the middlegame (unless they are advanced in which case they restrict the opponent)


Those are all of the strange imbalances I can think of off the top of my head.  I omitted things like rook and pawn vs two pieces or knight vs bishop because those are fairly common, and those especially depend on the position.  Again, every position needs to be considered on its own, this is just to get you in the right frame of mind when you have to make a determination.