One that we do, common in correctional facilities, where you use a deck of cards to do pushups (doing said number of reps on the card you draw.) This can be used for any exercise, such as dips or chinups. Face cards are worth 10 reps, aces are worth a short break.
Another one is "chicken", where me and my buddy who is about the same strength as me, pick up the same amount of weight and see who can out rep eachother. We set up 2 benches facing eachother, each grabbed a 45lb dumbell and started doing skullcrushers across from one another. The loser (first one to stop) must do 10 pushups. Do this for a few sets.
Anyone have any fun games they do to increase motivation and intensity?