My year-old rig runs the Crysis demo just fine, I tried it tonight. I am running at 1360x768 with 4xAA rather than 1920x1080, however. Still looks quite good, even with medium detail.
System specs: AMD 64x2 4400+, 2GB DDR400, Geforce 7950GT video with 512MB of RAM, Win XP (DX9).
EDIT: Played the demo all the way through to completion in ~2 hours. I think I’m going to have to get the full game. Using cloak mode to sneak up on guys, knock 'em out with a tranquilizer dart, then cap 'em with the silenced rifle is way too much fun. I did find myself wishing for a sniper rifle of some kind though.