I run a Core2Duo E6600 2.4GHz with 2GB Ram, 320MB Nvidia 8800GTS graphics which I built myself.
I only run games on one 19in monitor, at 1280x1024, but I've not seen a game yet which cannot run smoothly.
If you get to higher resolutions, I'd imagine a beefier graphics card would be needed. IMHO once you reach high-end specs, the graphics accelerator has a lot more impact on frame rates than processor.