NO (in general)- and YES (specifically) - there is a "50 move rule" in which the game is a draw if 50 consecutive moves are made without a pawn move or piece capture. (For instance, so that bozos who don't know how to mate with K+B+N vs K can't learn it OTB by making you sit at the board for days, wks or years until they "get it.") And there is a "triple repetition rule" in which the game is drawn if a player announces it prior to making his/her move that will result in a triple repetition of the exact same position - and it doesn't have to be three moves in a row either which can get confusing, esp in time pressure.
Other than that, the other reasons for ending a game don't directly relate to limiting the number of moves: checkmate, stalemate, insufficient material or both players simply agree to a draw.
Is there a limit to the number of moves in a tournement game?