What is the term for a stalemate in Checkers?
According to the American Checker Federation (see rule 12), a tie game is called a draw.  The conditions for a draw are similar to the 50-move rule in chess.  Basically, one player asks the other to prove he can win (or get closer to winning) in the next 40 moves or the game ends in a draw.  I imagine this would only really occur in high level play, perhaps by several kinged pieces moving endlessly around the board with neither side gaining an advantage.

A condition like a stalemate in chess (where a player has no legal move to make) results in a loss for the player whose turn it is to move.