Which game can Intel G33 G31 Express Chipset Family run?

Starcraft 1. Probably some stuff made more than 10 years ago. I think I've run Jedi Knight dark forces II, and maybe Morrowind. Not to mention minesweeper, duh.

For FPS check out Cube 1, or maybe some older versions of Sauerbraten (cube 2) will work, lots of people play that online.

Look for some sites that review good freeware games, but not arcade style, unless you want that. "indie" games are usually good.