Blitzkrieg Chess
Blitzkrieg chess is a variation which emphasizes speed above all else. While many of the rules remain the same (for instance, the aim is still to checkmate one's opponent), there are several notable differences. Blitzkrieg chess games typically have a time limit of ten minutes; if the clock runs out before a checkmate has been achieved the player whose turn it is must forfeit the game.
Another optional variation, called "Suicide Chess" can be incorporated into Blitzkrieg chess. Suicide chess rules dictate that if a player has an opportunity to take an opponents piece, he must do so, even if that would put him at a strategic disadvantage.
Fischer Random Chess
Also known as "Chess 960" (so called because it adds a possible 960 opening moves), Fischer Random Chess calls for all the pieces on the A and H flanks (that is, both players' rooks, bishops, knights, queens, and kings) to be placed in a random order. There are many ways to decide the random order of these pieces; one popular method is to use a 6-sided die, ascribing a number to each piece and placing the pieces in the order in which they come up on successive rolls of the dice.
Fischer Random Chess was invented by American Grand Master Bobby Fischer. The purpose of randomizing the order of the pieces is to force players to devise new opening strategies with each game. Fischer observed that, to a large extent, success at high level chess largely depended on a player's ability to memorize opening moves. Fischer Random Chess forces players to use more creativity during the crucial first phase of each game, leading to more open and dynamic games.
Anti-chess
Anti-chess is a variant in which the object is to be the first player to lose all his pieces; players must, however, take every opportunity to capture their opponent's pieces. There is no checkmate in anti-chess -- the king is treated as just a normal piece.
Crazy Chess
Crazy chess is an online animated chess game. The player, controlling a knight, is besieged by several waves of pawns which move down different flanks towards the back row. The object of the game is to use the knight to capture the pawns before they can reach the back row; if enough pawns reach the back row the game is over.