I know that it is makes no sense to promote a pawn to a bishop or a rook as the queen can compensate for both but a knight is something different. However, the queen is still much more powerful. So what situations would provoke you into promoting your hard-labored pawn to just a knight rather than a queen?
White to move:
Since my example is rather contrived and artificial, I'll also say that the so-called Lasker trap in the Albin Countergambit gives a more realistic setting, and one where a knight promotion is the best option as early as move 7:
Oddly enough, I happened across that line for the first time just earlier today.
Oh, and there are situations where underpromotion to a bishop or rook is necessary in order to avoid a stalemate that a queen might create. For instance, in the sequence of moves coming from the Saavedra position, if white were to create a queen with
After answering this question, I was reminded of another important situation where underpromotion is necessary:
In this position,
While this is a slightly contrived example, it does come in handy sometimes. As an anecdote, I was playing a rook and pawn endgame where I was up a pawn. In one variation, my opponent could sacrifice his rook for my last pawn and reach this position:
I was able to recognize that this is actually a draw because black can play
During round 9 of the Instanbul 2012 Chess Olympiads, at the Nakamura-Kramnik table of the USA vs Russia match, we've witnessed another one of those promotions to knight at move 62 by white.
The relevant position (white to play):
We can see here that if
and the bishop on
To avoid that, Nakamura promotes his pawn to a knight with check to save his advantage.
Here are 4 different commentaries of the game, pick your favorite one!
When you said it made no sense to promote to a Rook or Bishop, it brought this position to mind. Here, if White promotes to a Queen, the game is drawn, but if White promotes to a rook, White wins.
on 1. c8/Q Black would answer 1 ... Rc4+ 2, Qxc4 stalemate. But on 1. c8/R 2. Rc4+ White can capture the rook without fear of stalemate.
Sometimes the queen is not the most powerful piece available. Every position is different, and the extra move possibilities of the Queen can work against you sometimes. Whenever you promote, think. Most of the time, yes, a Queen is the best choice; but not always. Look around and see if a different piece would be better, or if there is a danger of stalemate posed by the queen's extra moves.
Here is a fun tactic, involving underpromotion, to finish off the game if you are two connected pawns up in a rook endgame. I saw this in an endgame manual a long time ago, but cannot find the source anymore. The tactic is totally unnecessary as white has other ways to win. Still, it's quite impressive.