There are hundreds of variants to the normal game of chess. Here are just some of the chess variants.
3D Chess or Star Trek Chess– The three dimensional board consists of seven different levels. Three of these levels have size 4x4 and have a fixed position. The four other levels have size 2x2 and can be moved by the players. The position of the fixed levels looks like a staircase.
Accelerated Chess – Each player makes two non-capturing moves or one capturing move in each turn.
Alice Chess – Two chessboards are used. One is set up normally and the other is empty. After moving a piece, the piece is transferred to the corresponding square on the other board. Each player makes a single move on either board. A move must be legal on the board where it is played. A piece can only move or capture if the corresponding destination square on the other board is vacant.
Bughouse Chess - Two orthodox chess boards are set up for four players. One player on team A has White and one player on team A has Black. Team B then has someone playing Black on one board and another player playing White on the other board. All captured pieces are given to one’s partner. Once received, they become reserved pieces which can be dropped onto an empty square on the board to be used as one’s own pieces. You may not advise your partner, but you can ask him to capture a certain piece that you need. You can say, “Partner, I need a knight.”
Checkers Chess – The normal rules of chess apply, but pieces can only move forwards until they have reached the last rank.
Checkless Chess – Players are forbidden from giving check except for checkmate.
Chess960 or Fischer Random Chess – The initial setup of the pieces are chosen randomly. The pawns are placed on their normal squares. The remaining pieces are placed on the first rank. The king is placed somewhere between two white rooks. The bishops are placed on opposite-colored squares. The black pieces are placed equal-and-opposite the white pieces.
Circular Chess - The game is played on a circular board made of 4 rings of 16 squares each. A normal set of pieces are used and the standard setup is folded along the round board.
Courier Chess - This is a game played on an 8x12 chess board. Players have 24 pieces: 12 pawns, a king, a queen, a counselor, a spy (or fool), two couriers, two bishops, two knights and two rooks. The counselor moves one square at a time like a king, but without being hindered by check, etc. The spy moves one square horizontally or vertically. The courier moves like a modern bishop. The bishop jumps two squares diagonally. The game was played in Germany in the middle ages.
Giveaway Chess – Pieces must be taken if possible, so capturing is compulsory. There is no check or checkmate. The king plays no special role in the game and can be taken as any other piece. The first player that loses all his pieces wins. The game is also known as Losing Chess or Suicide Chess.
Handicap Chess or Chess With Odds – One player will play without a pawn or a knight or a rook or a queen, It is a game of chess that enables a weaker player to have a chance of winning against a stronger player. Various permutations include things like “Pawn and two moves,” are also possible.
Hexagonal Chess – The game is played on a hexagonal board. The board has 91 hexes with three different colors. There is an extra bishop and pawn for each player.
Kriegspiel – This is a battle between two players. However, a third person is needed to act as a referee. One needs three boards for the game. The main idea is that players only get to see their own pieces, but not see the pieces of their opponent, and do not know what moves the opponents has made. Only the referee knows exactly the real position of both sets of pieces. Players move like normal chess. Each turn, a player attempts a move. When the move is legal, the referee announces that the player has moved, and the turn is done. When the move is illegal, the referee says so and the player must make a new attempt to move until a legal move has been made.
Marseilles Chess or Two-move chess – After the first turn of the game by White being a single move, each player moves twice per turn.
Progressive Chess – The player with White moves once, the player with Black moves twice, the White player then moves three times, etc.
For more on chess variants, see http://www.chessvariants.com/