My favorite variant is Twilight Chess [1]:" The general idea of twilight chess is fairly simple : you can move any of your piece, but the king, into a twilight zone (warp moves), and any piece on the twilight zone may be moved to any empty square of the board (drop moves), but pawns on the last rank. "

[1]: http://membres-lig.imag.fr/prost/Twilight_Chess/index.html