Even with my lowly P4 2.4 ghz, 1GB RDRAM, and 6600 GT OC, I still manage to run all my games at either 1600x1200 @75hz (fine for my eyes), or 1280x960 with 2xAA 4xAF. The latter is usually just a tad less smooth than the straight up 16x12, but it's also a tad prettier. So I'm constantly experimenting, seeing which game handles which setting best. BTW, I use a 19" CRT.
My goal is to build a solid rig next summer ($2,000-3,000 range) with dual video cards and be able to play 2048x1536 with full image processing at 60 fps. Just waiting on technology... and my bank book.
EDIT: Most games I run are older, like HL2, Raven Shield, FS2004, San Andreas, and Operation Flashpoint. But I managed to play the Call of Duty 2 demo just last week and got maybe 30 fps at 1280x960. I'm constantly surprised how well my 3.5 year old system (save the video card) hangs in there.