The "worth" or "value" of any piece is always situational. The concept of sacrifice includes compensation for the side losing material. That compensation may not be a material return, but something else like weakening enemy king safety, for example. Therefore, I prefer to consider a piece's "strength" as its usefulness in a given situation, rather than a number.
Generally, bishops become stronger than knights into the endgame, when the position is more open. Knights can be stronger than bishops in the opening and middle game when positions could be more closed and cramped. These ideas guide my considerations of B/N exchanges.
A pinned piece has a reduced value since its movement options become limited or negated altogether. (If a bishop or undeveloped rook are considered "bad" so too would a pinned pawn be bad and not as strong)
In the endgame, the king's "value" has been approximated to 4 pawns. (I don't recall the source). Usually in the endgame, you try to quickly centralize your king to strengthen him.
A pawn that promotes effectively adds only 8 pawns of value for the side promoting (+9 for the new queen, -1 for the removed pawn).
Any piece near the center is stronger (can move to more squares and/or more directions).
An edge pawn can only capture on/protect one square. It isn't as strong as pawns on files b-g.