The fifty move rule in chess states that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves. The relavent part of the official FIDE laws of chess is rule 9.3:
The game is drawn, upon a correct claim by the player having the move, if
a. he writes on his scoresheet, and declares to the arbiter his intention to make a move which shall result in the last 50 moves having been made by each player without the movement of any pawn and without the capture of any piece, or
b. the last 50 consecutive moves have been made by each player without the movement of any pawn and without the capture of any piece.
It should be noted that after fifty moves the game is not automatically a draw--the draw must be claimed by the player on move. It is, therefore, possible for a game to continue beyond a point when a draw could be claimed under the rule.
The rule has a long history, with Ruy Lopez' 1561 text on chess including details of it. In the 20th century, with the discovery that certain endgames (such as two bishops and king against knight and king) can only be won in more than fifty moves from certain positions, the rule was changed to include certain exceptions in which one hundred moves were allowed with particular material imbalances. All these exceptions were later scrapped and all material combinations are now subject to the fifty move rule.
Games drawn under the fifty move rule before the endgame are rare. One example is Filipowicz - Smederevac, Polanica Zdroj 1966, which was drawn on move 70 without any captures having been made in the whole game and with the last pawn being moved on move 20.