Chess variants are games related to chess but using either additional pieces, different starting positions, a different number of players, or different rules. More details can be found on this wikipedia page, or in The Classified Encyclopedia of Chess Variants, by David Pritchard, available in PDF.
Lichess allows to play several chess variants.
When creating a game against the computer, even if you are not registered, you have the choice between the following chess variants:
Crazyhouse
In the Crazyhouse variant, the capture pieces change color and can be dropped on an empty square by the capturing player instead of making a move, with the restriction that a pawn cannot be dropped on the first or the 8th rank. This is similar to the dropping rule in Shogi, a japanese game similar to chess.
Chess960
Chess960, also known as Fisher Random Chess, is a variant where the initial piece position is randomized (but is the same for Black and White). There are 960 possible initial positions.
The rules of castling are different in ths variant, and can be found here.
This variant is quite popular nowadays, with tournaments organized event between strong chess players.
King of the Hill
In the King of the Hill variant, a game is won by the player who checkmates his opponent, as in standard chess, but also by the player who brings his King to one of the 4 center squares.
Three-check
In the Three-Check variant, the player who checks his opponent three times wins the game. This means that sacrifying pieces can be done more easily if it guarantees the possibility to give checks.
Antichess
Also called losing chess (and many other names), the goal in the Antichess variant is to give up all one’s pieces. Taking is mandatory, and the King is behaving like a normal piece (he doesn’t have to escape checks and can be taken as any piece).
Atomic chess
In Atomic Chess, any capture results in removing from the board the captured piece or pawn but also the capturing piece and the pieces (and not the pawns) located on the 8 squares around the capture. This implies that the capture of a piece next to the opponent King ends the game by “capturing” the King.
Horde
In Horde Chess, White starts the game with 36 pawns while Black has the usual pieces. The goal for Black is to take all White’s pawns, while the goal for White is to checkmate Black (White’s pawns can be promoted as usual).
Racing Kings
In the Racing Kings variant, the initial position is the one shown on the picture. The winner is the first player to get his King reach the 8th rank.
From position
This is just playing with the standard rules but from a different starting position. It can be useful to train yourself to win in some winning positions (for example, you may want to lear how to win with a King and a Rook against a lone King).
Conclusions
Lichess allows to play several chess variants. Have you tried any of them? If so, please let us know in the comments below.