Some really stupid versions of push ups. Also known as great fun.
Elevated feet push ups. Simply having your feet on something above ground level, this can include a bosu ball, bench, or suspended straps.
Obviously with clap, especially if combined with the above, favourite of mine is with straps lifting feet, so you end up swinging while clapping with no fixed idea where your hands will land.
Hands on bosu or pumped medicine ball. Unstable exercise for unstable minds.
Bosu with lift off and chest touch. Bosu with platform facing up hands on the edges, down to touch chest against bosu, blast off straightening the arms to be able to bring the bosu off the floor and to your chest, then extend but not fully straighten the arms to catch yourself. Personal favourite at the moment is this with a small medicine ball, raw stupidity in motion.
Some more sensible and safer options.
Slow movement. Exactly as Famas says.
One hand on a medicine ball, press up then switch ball to the other hand.
Adjust width and angle of arms. The chest brings the arms together so the more of this you are doing the more chest you are using.
Single arms, various forms of this.