Total moves possible in Chess?

Has anyone ever figured out how many games/moves are possible in chess?  There should be some easy formula right?  With a cutoff for obvious draw situations like a white king & bishop/knight chasing around a single black king.

Infinite number, even if you forbid making a move, undoing it, and making it again entirely (even for ``a move'' equalling any number of actual moves on the board). It's not terribly hard to see why (in fact, it's a lot like realising why an irrational number can exist in a finite number base), but proving it is rather too much effort right now.
Just try to devise a strategy for counting games, you'll run into it quickly enough.