There are some quite interesting games played with a chessboard and pieces apart from chess. Some of them can be played on the Internet Chess Servers. Here is a quick overview of the rules.

SUICIDE CHESS ("takeme") The object of the game is to lose all your pieces (and pawns). If you can take, you have to, though you may choose what you take. The king can be taken, there is no check. Stalemate is a win for the stalemated side. The golden rule is to keep things undefended.

PROGRESSIVE White has 1 move, Black has 2, white has 3, black has 4 etc. A move stops when check is given. Players have only one move to escape check, else they are checkmated.
A variation on Progressive is a variant in which you can make up to 10 moves a turn (White has only 5 on the first move), but cannot move the same piece twice. In addition, whenever a capture is made, the opponent has the option to recapture on that square.

TRANSFER or BUGHOUSE 2 teams of 2 players play on adjacent boards, each team having one white player and one black player. Whenever a piece is taken it is passed to the partner of the capturing player. One captured pieces may be dropped on any vacant square at any point (even to escape check) instead of moving. One variant dissallows pawn promotion. Initiative is all important (e.g. droppong pieces on with check is very powerful)

KRIEGSPIEL 2 players plus an umpire use 3 boards and sets. Players know where their own pieces are but don't know where the opponent's pieces are. The umpire keeps track on a third board. Players 'try' moves including up to 3 pawn captures in an attempt to learn about the opponent's position. If a player tries a move and it is legal then that move must be played.

GOCHESS (Invented by Bill Jordan) A new chess variant which combines features of chess and go. Players start with a full set of pieces and an empty board and alternately place a piece or pawn on any square not attacked by the opponent. If there are no safe squares then you have lost. In the unlikely event all pieces have been placed, the game is drawn. The king must be placed on your first turn. Your second bishop must be placed on the opposite colour to your first. Pawns must not be placed on the first or 8th ranks. Attacking a piece already on the board has no consequence. Easy on the first few turns, the game is quite a challenge to play well.

Many other chess variants are mentioned in the book "100 Other games to play on a chessboard" by Stephen Addison. This book also includes games other than chess variants.

COMPELLED CAPTURE CHESS You must capture if you can.

FORWARDS CHESS A piece can never move backwards.

Some other chess variants I have invented include:

SIMULTANEOUS CHESS Each player writes down a legal move. Both moves are revealed and they are played simultaneously. If 2 pieces take each other, both go off the board. If a piece tries to take a moving piece, there is a standoff, players try different moves.

AVOIDANCE CHESS A piece/pawn cannot make 2 moves in a row. (including to escape check or mate).

FREEDOM CHESS Only moves that are a result of white or black's last move can be played. (A player's first turn is normal.)

For example, a game begins with 1.e4 e5 Possible second moves for white are Qe2,Qf3,Qg4,Qh5,Be2,Bd3,Bc4,Bb5,Ba6,Ne2 and Ke2

JUMP CHESS Queens, rooks and bishops can optionally jump over 1 intervening piece of either colour.

DOUBLE CHESS Each turn, you make one legal move for yourself, then one for the opponent. The move you for the opponent cannot undo his last move.

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