According to my reasonably large database, at least 3 players have been mated in 2 moves. They all lost to variants of 1.f3 e5 2.g4 Qh4# A few more players have lost in 3 moves to the same kind of mate. I'm assuming they were all deliberate losses, especially the game that went 1.h3 e5 2.f3 Qh4+ 3.g3 Qxg3#
Of course the venerable "4 move checkmate" may well be the most popular quick checkmate ever, although the majority of tournaments it occurs in are likely to be using scoresheets.
Moving up to mate in 5's, the trap in the From gambit has claimed a few victims (1.f4 e5 2.fxe d6 3.exd Bxd6 4.Nf3 g5 5.h3?? Bg3#), while smothered mates on d3 and d6 start to turn up. 6 moves mates are still mainly Qxf7/f2 and Nd3/d6, but by move 7 we get to some cleverer mates. The Blackburne Schilling Gambit starts to show up (1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4?! 4.Nxe5?! Qg5 5.Nxf7 Qxg2 6.Rf1 Qxe4+ 7.Be2 Nf3#). You also see some more 'normal' mates, with attacks on the castled king now becoming possible.
Past move 8 it is pretty much a free for all. Certainly there are still traps for the unwary, but it is more a case of exploiting a blunder, rather than playing for a specific mate.
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There is also the mate trap in the Budapest
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