I actually discovered a mate by a rook in 4.5 moves WITHOUT promotion! My source is this page with lots of other interesting shortest checkmates.
This made me wonder what the fastest bishop and knight checkmates by promotion are (DM’s answer has that for the rook. It works just as well for a queen!) I also saw these and an even shorter pawn checkmate then what DM has on the same site.
Let the show begin!
Shortest Non-Promoted Rook Checkmate:
1.a4 c5 2.a5 Qxa5 3.Rxa5 c4 4.Rc5 c3 5.Rxc8#
Shortest Pawn Checkmate (Many varieties exist):
1.e3 e5 2.Ke2 Qh4 3.Kf3 f6 4.Be2 e4#
And just because pawns have other moves (This site is the source and it has tons more!) here’s the fastest double step pawn mate:
1. c4 d6 2. Qb3 Kd7 3. e3 Kc6 4. Qxb7+ Kc5 5. d4#
Shortest Knight Promotion Checkmate
1.h4 d5 2.h5 Nd7 3.h6 Ndf6 4.hxg7 Kd7 5.Rh6 Ne8 6.gxf8=N#
Shortest Bishop Promotion Checkmate
1.d4 g6 2.d5 Bh6 3.d6 Kf8 4.dxe7+ Kg7 5.Qd6 Qf8 6.exf8=B#
Then again, those are checkmate with promotion. If you want it without promotion, I found these ones on my own. If you know of a faster one (I’m staring at the knight one), please do let me know.
Shortest Promoted Bishop Checkmate
Another Update: As I figured, @DM found a faster bishop one!
1. d4 c5 2. dxc5 Qb6 3. c6 Nh6 4. cxb7 Nc6 5. bxc8=B Nd8 6. Bxd7#
(Again, this also applies to the queen!)
1. e4 f5 2. exf5 g5 3. fxg6 Nf6 4. g7 Ne4 5. g8=B h5 6. Bh7 h4 7. Bg6#
(The same process goes for a promoted queen: 1. e4 f5 2. exf5 g5 3. fxg6 Nf6 4. g7 Ne4 5. g8=Q h5 6. Qg6#)
Shortest Promoted Knight Checkmate
Update: @DM found one better than me as I suspected was possible!
1. g4 Nc6 2. g5 e6 3. g6 Nce7 4. gxh7 g5 5. hxg8=N Rh3 6. Nf6#
1. e4 f5 2. exf5 g5 3. fxg6 Nh6 4. g7 Nf7 5. g8=N h6 6. Qe2 h5 7. Nf6#
Shortest Promoted Rook Checkmate
1. g4 h5 2. gxh5 g6 3. h6 Bg7 4. hxg7 Nf6 5. gxh8=R+ Ng8 6. Rxg8#
(This also applies to the queen!)