One varient chess I made up some time ago and still play periodically is "The Crown of Krithala" -- it can be played with any varient game that has kings, though I normally play it with standard chess.
Each player begin the game with a checker of the appropriate color under their king. This is the "crown". The objective of the game is not to mate the King but to capture the crown.
The crown starts with the King, and has no effect on the King's movement, but it can be moved to any piece -- though it does effect how the piece can move.
A player may transfer the crown to another of his pieces using a move the same as the piece currently carrying it. This does not change the location of the former carrier, just that of the crown -- and the transfer counts as a move. Thus a king standing next to a knight could transfer the crown to the knight. A knight could move the crown to a piece at the end of any valid knight move it can make (and would not be able to immediately transfer it back to the King.) The crown may also be dropped on the square it is on and the carrying piece moved away -- the crown could be picked up later by another piece, and it cannot move on its own. Dropping or picking up a crown does not count as a move and can be done even in passing (as in a queen passing over a dropped crown and picking it up while on the way to her destination.
Special rules: aside from the King, no piece carrying the crown can move more than twice in a row. That is, some other piece must move on that players turn between moves of the piece carrying the crown. The crown drops automatically on the starting square of the third move in a row. A piece that has dropped the crown cannot pick it up again until has been dropped by another piece. Finally, the crown cannot be transferred twice in a row -- it must be moved by the carrying piece. These rules make it unlikely that someone could transfer the crown to a queen and indefinitely postpose losing it.
It's a fun variation.