Depends on the game. For really twitchy FPSs, you'll want at least over 40. UT2k4 players (and others... just I had a lot more interactions with them) would bitch and moan about sub-60 fps.

The scary thing is that they weren't always bullshitting about that.

Also, as sister reply said, going at 60 means no screen tearing on -anything-. Don't need to vsync, or anything nasty. TVs, computer monitors, projectors, cellphones, whatever, one whole new frame per refresh. yum.