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:
[FEN "8/q1P1k3/8/8/8/8/6PP/7K w - - 0 1"]
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:
[FEN ""] 1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 $2 Bb4+ 5.Bd2 dxe3! 6.Bxb4 $4 exf2+ 7.Ke2 fxg1=N+ $1 8.Ke1 Qh4+ 9.Kd2 (9.g3 Qe4+) Nc6 $19
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
6. c8=Q, this would allow black to draw by stalemate, and so white must instead play
6. c8=R in order to win:
[FEN "8/8/1KP5/3r4/8/8/8/k7 w - - 0 1"] 1.c7 Rd6+ 2.Kb5 Rd5+ 3.Kb4 Rd4+ 4.Kb3 Rd3+ 5.Kc2 $1 Rd4 $1 6.c8=R $1 (6.c8=Q $2 Rc4+ $1 7.Qxc4 $10) 6...Ra4 7.Kb3 $18
After answering this question, I was reminded of another important situation where underpromotion is necessary:
In this position,
1...b1=N+ is the only move to draw. Any other move will allow a quick mate, but after knighting the pawn, black sets up a drawing fortress.
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
1...b4 2.Rh4+ Kc3 3.Kc5 b3 4.Rh3+ Kc2 5.Kc4 b2 6.Rh2+ Kc1 7.Kc3 reaching the position above. Due to this, I went into another variation and won. Without knowing this idea, however, it would have been very hard to resist winning my opponent's rook.
During round 9 of the Istanbul 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
62. ... f3+
and the bishop on
g3 will take the
c7 pawn next move resulting in a draw.
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!
There are even positions where one promotes R or B to save a draw by getting stalemated (rather than win by avoiding stalemate). One example is the Traxler-Dedrle setup:
[FEN "4rN1K/5qP1/8/8/8/8/k7/8 w - - 0 1"]
WTM loses with 1 g8Q? Rxf8 2 Qxf8 Qxf8+ but draws with 1 g8B!! when Rxf8 is stalemate (NB the g8B pins Qf7).
There's a famous study by Rusinek where White must promotes both R and B (as well as N) to guarantee a draw; see the position shown in Rusinek's Wikipedia page https://en.wikipedia.org/wiki/Jan_Rusinek.
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.
If you are down on time, and see a mate-in-1 with an additional knight? :-)
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.
[FEN "r6k/8/6PP/5RK1/8/8/8/8 w - - 0 1"] 1.Rf8+ Rxf8 2.g7+ Kh7 (2...Kg8 3.Kg6) 3.gxf8=N+!(3.gxf8=B!)(3.gxf8=Q??)(3.gxf8=R??)
1.Rf8+ Rxf8 2.g7+ black doesn't play
2...Kg8 because of
3.Kg6 and mate next move (
4.h7#). Instead black plays
2...Kh7 hoping for stalemate. Then
3.gxf8=B! both win, while
3.gxf8=R?? lead to immediate draw.
Here, 29. ... Ba3+!! and promoting to knight could've save the game!
[Date "2012.05.12"] [Result "1-0"] [FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"] [White "Ni Hua"] [StartPly "57"] [WhiteElo "2673"] [Black "Le Quang Liem"] [BlackElo "2703"] [Event "Asian Continental Open Championship"] [Site "Ho Chi Minh City"] [Round "8"] [ECO "B84"] 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 e6 7.Be2 Qc7 8.g4 b5 9.g5 Nfd7 10.a3 Bb7 11.Qd2 Nc6 12.Nxc6 Bxc6 13.f4 Nc5 14.Bf3 Qb7 15.Qd4 e5 16.fxe5 Ne6 17.Qd2 dxe5 18.Nd5 Bd6 19.O-O-O O-O 20.h4 a5 21.h5 b4 22.h6 bxa3 23.b3 Rfc8 24.Nb6 Bb4 25.Qh2 Bxe4 26.hxg7 a2 27.Kb2 a4 28.c4 axb3 29.g6 Ba3+!! 30.Kxb3 a1=N+!! 31.Rxa1 ( 31.Kc3 Rxc4+!! ( 31...Bb4+! 32.Kxb4 Ra4+!! 33.Kc3 ( 33.Kxa4 Nc5+ 34.Bxc5 Qc6+ 35.Ka3 Qxc5+ 36.Ka2 Qa5+ 37.Kb2 Qxb6+ 38.Kxa1 Qa5+ 39.Qa2 Qc3+ 40.Qb2 Ra8# ) 33...Rcxc4+!! 34.Kd2 ( 34.Nxc4 Qb4# ) 34...Ra2+ 35.Ke1 Rxh2 ) 32.Kd2 ( 32.Nxc4 Qb4# ) ( 32.Kxc4 Qc6+ 33.Bc5 Qxc5# ) 32...Rc2+ 33.Ke1 Rxh2 ) 31...Qxb6+!! 32.Bxb6 Nd4+!! 33.Kc3 ( 33.Bxd4 Rcb8+ 34.Kc3 ( 34.Ka2 Bc5# ) 34...Bb4+ 35.Kb2 Bd2+ 36.Bb6 Rxb6# ) 33...Rxc4+!! 34.Kxc4 ( 34.Kd2 Nxf3+ 35.Kd1 Nxh2 36.Rxh2 fxg6 ) 34...Rc8+ 35.Bc5 Rxc5# 0-1