i think in the 19th century, if you touched a piece that could not move you had to move your king. A player touched a bishop that couldn't move and was mated on move three. the game went 1 e4 d5 2 exd5 Qxd5 3 Ke2 Qe4 #
Shortest GM checkmates

There's one, unfortunately it's blitz as far I could find. It involves a very big name as victim...
http://www.chessgames.com/perl/chessgame?gid=1599669

I think there's a YouTube video somewhere with about five or six of these. Haven't time to find it and post the link but some other kind soul might do so.

Gibaud vs Lazard 1924 reportedly finished in 4 moves with a black win from a Budapest gambit trap I think but there are doubts about the authenticity of this game. Also the famous Reti - Tartakower game from the 20's.
Larsen vs Spassky, USSR vs Rest of the World (1970)
Game 2 of the match: Larsen resigns after 17 moves.

GMs tend to resign when they go down major material in the opening (say a piece or even a few pawns) or are about to be mated. Most forced mates in the opening come from traps that GMs know. As such, I doubt you'll find much that meets your criteria of GMs getting mated very early. Sometimes GMs allow themselves to be mated to allow their opponent to finish off a brilliant combination if it leads to forced mate, which is almost certainly what happened in the Reti game above.
The shortest GM loses I know are when Anand lost in 6 moves to GM Zapata: 1 e4 e5 2 Nf3 Nf6 3 Nxe5 d6 4 Nf3 Nxe4 5 Nc3 5…Bf5?? 6 Qe2 which wins major material, so Anand resigns.
I've read that the shortest loss by a titled player was an IM who lost after d4/Nf6, Bg5/c6, e3??,Qa5+, winning the bishop and forcing immediate resignation
Sometimes it happens that GMs have bad days and blunder pieces or positions such that the game is lost in the opening. This is very humorous, but not what I'm interested in.
Does anyone know examples of games where a GM is either checkmated in the opening or resigns due to forced checkmate? I am not talking about resignation due to material loss, but actually overlooking a forced checkmate in the opening due to some combination. Does this ever happen, or are GMs pretty much immune to this? Anything before move 15 is fine. And again, I don't mean a game where somebody plays a losing move before move 15, I mean a game that, if continued by best play, would end in checkmate by move 15.
I have never seen such a game and I wonder if they exist.