Two years ago I talked about a spherical chess variant [1]. Now, I want to mention real time chess [2], where players can move their pieces at will, with the only limit being once a piece is moved, you can't move it for five seconds. And there's no check or checkmate—you win by capturing the opponent's king.
The problem with real time chess is that you really can't play it on a real board, since you would have to trust the other player not to move a piece immedately after moving it (and the other player would have to trust you to do the same). That is, unless you have a special chess set [3] built just for the game. It's a cool set—the board and all the pieces are metal, with each square having an electromagnet to hold the piece down, and LED (Light Emitting Diode) lighting to indicate when a piece can and can't move. But no mention of the cost—it's probably one of those “if you have to ask, you can't afford it” type things.