A player may claim a draw after 50 moves.. does this mean 25 moves by each player (which results 50) or 50 moves by each player (which results 100)?
From the FIDE rules (emphasis added):
The game is drawn, upon a correct claim by the player having the move, if:
a. he writes his move on his scoresheet and declares to the arbiter his intention to make this move, which shall result in the last 50 moves having been made by each player without the movement of any pawn and without any capture, or
b. the last 50 consecutive moves have been made by each player without the movement of any pawn and without any capture.
So it's 100 total plies, or "half-moves."
An interesting detail of the 50 move rule: As only the player to move may claim a draw (either by declaring that the 50 move limit has been reached or by declaring his intention to make a move after which the limit will be reached), if the 100th half-move that is not a capture nor a pawn move is a checkmate, then the game is not drawn. See e.g. Arbiter's notebook 98.