>>10
My favorite ones are those that doesn´t need to change the board, so you can make new games with the same materials.
>Knight Relay
A piece defended by a knight of its colour gain the knight´s jump. The knights themselves can not be taken nor take other pieces.
>Knightmate Chess
Instead of a King, a Knight, instead of the Knights, two Kings.
Knights are amazingly easy to checkmate, since can´t attack any piece next to them and has to run away to the centre.
Kings are very useful attack pieces, but slow to activate.
(Pic related)
>Extinction
Any player who loses all pieces of any specific kind (eg the two bishops, or the one queen, or the eight pawns), loses the game.
And of course, the mighty one:
>Fischer Chess/960 Chess
I wouldn´t call this a variant though, but classical chess a variant of 960 Chess.