FoldIt (beta) is a type of online game I'd never heard of before yesterday. It was released last month (here's the Wikipedia entry to prove it).It's essentially a clever way of enlisting people to help predict protein structures (by folding them) -- even if all they know about proteins is that you should eat them after exercising.
I checked out a few multiplayer games, but wanted to find something that wasn't just frivolous. Skill-building games like Scrabulous or TypeRacer are good, but FoldIt goes beyond honing personal skills to possibly contributing to cures for diseases, like HIV (and being a candidate for Nobel Prize!).
It's free, but not entirely online. You download a client to your computer, go through some sample puzzles to get the hang of it, and then you can join groups that are working collaboratively, or compete with people around the world as an individual.
Each structure is a complex, 3D puzzle that behaves in strange ways.
Competing with others online is kind of intimidating but all you're seeing is their ranked scores, and you can chat with them within the FoldIt interface.
It is a well designed game, and an ingenious concept, and it's extremely challenging!
Recommended (may result in losing all sense of time)