While I am a fan of nearly all board games, I've just never gotten excited about Go, the subject of the most recent human-computer smackdown. But a couple of days ago, Andre Ranchin proposed an amusing variant of Go -- one that incorporates quantum mechanics!
You can read the full description of the game here, but the basic idea is that instead of putting down single stones, each player can put down a quantum-entangled pair of stones. In line with the way that quantum mechanics works, the stone can be in either of two locations until the wave function collapses on a later turn, forcing the stone to be in one place or the other. It's a a fun idea -- I don't know if it makes an interesting game. But it might be a good way to teach quantum mechanics to children.