UT2003 actually ran at a decent clip on my older machine (with a GF2mx). It certainly didn't run great, but it was quite playable in medium detail (and that was with a 733 MHz CPU).
If you have not played them, System Shock 2, Thief II, and Deus Ex are all GREAT choices. Those are my 3 favorite FPS games of all time (even though they aren't exactly standard FPS titles).
Outside of that, it's hard to say. There really haven't been a whole lot of great PC FPS games released over the last few years. Lots of lackluster junk as well as a few solid titles with higher requirements...