Eg:
Madman chess

I don't think I really like it, but the name suits me quite well, so what the heck.
Question: Are all of your pieces required to move? That can lead to some interesting zugzwang very early on.

All of the peices that CAN move without having to wait for another peice to get out of the way first.

Cool. Let's do this. I was too lazy to get a coin so I flipped my cell phone. It landed face down so you get white.
I created this variant to see what would happen if you tried to play a game of chess in real(ish) time, as if it were a real battle.
Normal rules apply except each turn players move all of their peices symaltaniously. A player may NOT move one peice then move another through the space that was opened by the first peice moving (eg; on the first move you may not play pawn a4 then rook a3.) If a peice is unable to immediately move it remains stationary.
I think rather than keep track of ever move it would be easier to play by just posting the board with all your peices moved when it's your turn. Anyone want a game?