As a general baseline, to run any 3D game of the past year or year and a half at a half-decent level, you're going to need the fastest processor you can get (as khana says 1.5GHz or above), and 1GB RAM, together with a dedicated graphics card like the GeForce 5500 or above.
If you want to run an older game, then it'll run OK on cheaper hardware. Something like Quake II or Half Life (the first one) should run OK on your computer as it is now, but it'll be jumpy I'd guess. Just doubling the RAM and graphics memory would sort this though (assuming the graphics memory is on a dedicated card)