Most answers here talk about computer assistance, but I think the OP was asking about knowingly make illegal moves, which happens from time to time at club level (I cannot think of any GM-level example apart from Kasparov's touch-move rule against Polgar, see BlindKungFuMaster)
- I have once seen a pawn on f3 advancing to f5, with mate! That happened in a slow tournament game, and the "checkmated player" accepted his loss.
- In Blitz, I know a player whose pawns run faster than most of his opponent's in pawn-race endgames. It's probably due to them moving multiple squares at a time. The same happens sometimes with the king.
- I've also seen a knight on f4 moving to h6, with mate.
- Finally, in a game between two masters (not GMs, though), one of them claimed a stalemate that didn't exist. His opponent accepted the draw