Is there any better play than the 3-move mate? I know how to cause a checkmate in three moves. Are there any better ones? I've been told that  there is a two move one but, I have never found someone who can do it. Is it just a legend that has happened once or twice?
There is a two-move mate: the Fool's Mate. However, it requires White to be, as the name implies, extremely foolish!

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1.g4 e5 2.f3 Qh4#


As you can see, this mate relies on White advancing pawns without any regard for his King's safety. There's no way to force a two move checkmate (if there were, Chess would be an awfully boring game!).

As to whether it's ever occurred in real (master) play, I can't find any record of it, though the Wikipedia article mentions Teed vs. Delmar, 1896, where a very similar mate is delivered a few moves later.