How about the scholar's mate? it's four moves
less than 20
Isn't the scholar's mate the same as fool's mate.
No. However, the scholar's mate is oftentimes mistakenly referred to as the fool's mate.

Many examples from chess.com players can be found here:
http://www.chess.com/forum/view/game-showcase/checkmate-in-20-moves-or-less?page=1
Does anyone know of some good game's with a winner in less than 20 move's.