4-player chess (also known by various brand names) can be an adaptation of chess to 4 players. It is played on a board that is 8-by-8 but with a 3-by-8 extension on each side, so that it appears like a cross.
Rules
Pieces are put as in a normal chessboard at each player's first row in the extensions. The king and queen placement varies. Pawns move forward and attack diagonally forward only. You're allowed to use en passant. Castling is done exactly the same way as in normal chess. Pawns may promote upon reaching any player's first row. A player may only respond to check up on his/her own turn. Similarly, 4 player chess is only validated on that player's turn. A stalemate is when the player whose turn it is cannot move. A checkmated player leaves the game, but his/her pieces stick to the board (although they can not move). The last player standing wins. In a variant, the king is captured like any piece instead of checkmated, and the capturing player gets to use the captured player's pieces. Additional rules are often put into prevent teaming with other players. Team games can also be played. Players at opposite sides of the board are teammates, and cannot capture each other's pieces, and a king is considered in check if an opponent piece can is attacking it. The overall game has ended when both players of one of the teams are eliminated.