Game Idea: Backwards Chess
Basically, if it would be a legal move to go from gamestate X to gamestate Y in normal Chess, you could go from gamestate Y to gamestate X in backwards chess. The 'goal', which I suppose would have to be slightly cooperative, would be to get all the pieces of both sides into the normal chess starting positions (This variant starting with just a few pieces in a proper 'checkmate' position). The real goal would be to horribly confuse all onlookers, of course.

Interestingly, if the king moves "into" check, the other player must move out of it. Because it wouldn't be a legal move otherwise. Hmmm. That might actually be a good way to establish an actual competitive goal, get it so they can't get your king unchecked in their next move. That also provides good incentive to "uncapture" pieces, which would be moving a piece away from a square and leaving an opponent's piece there. And, hmmm, you couldn't move a piece INTO a location which 'checks' the other king, because that would imply, if you "restored" the proper turn order, that they moved themselves into check somehow. Interesting.

Now I need a chess set and somebody to test this idea with. Hmmm.