My longest game so far is
Game 1078193 against Meman, which lasted 124 moves. In fact it would have probably gone on a lot longer had Meman not been kicked off the site for engine use. I was awarded the game, even though the final position is only a draw despite the material advantage (Q+2P v Q). I certainly intended playing on as long as I legally could if only to spite an opponent who was clearly using an engine.
The whole game was in fact quite weird. I managed to make a 'mouse slip' on move 5 (I meant to play 5.Nge2 not Qe2) and lost a pawn for nothing. Then I chucked in a second pawn in an attempt to get some play but really didn't have much compensation until Meman (rather typically for a computer) greedily forced me practically to sacrifice an exchange. Fortunately, this proved to be very strong and allowed me right back into the game, and after a forced sequence of moves, I emerged with Q, N + a+b Ps v Q + R. This should of course be drawn, but I intended to play on a while, since I could hardly lose and my knight stood quite actively. However, I was amazed that, on the first opportunity (move 63), Meman voluntarily gave up the exchange, leading to the endgame Q + 2P (a+b) v Q.
Then I vaguely remembered having shortly before read an article by John Nunn in which he presented various endgames whose assessments had been changed by the advent of the silicon monsters. One of these turned out to be exactly the endgame above (namely Q + NP + RP v Q), which was originally considered an easy win but now reassessed as a draw in most cases where the defending King is not cut off from the pawns' queening squares.
Clearly, Meman's engine was equipped with the latest endgame theory and preferred to defend an endgame it 'knew' to be a draw than play on in a position, which though drawn, might have been assessed by the engine as slightly better for white.
No human player would dream of playing like that, since the techical draw that computers have found in this endgame requires only moves at a number of critical stages. Incidentally, if anyone wishes to have a good look at this endgame themselves, one of the main reasons it is drawn is that the defending side always seems to have stalematting resources when the pawns (ot the attacking King) get too far advanced.