My stats...

[SHRED]

P4 2.53 @ 533 FSB
Intel Blue Mountain 2 D845PEBT2 mobo
1024 MB (DDR SDRAM)
RADEON 9800 PRO (128 MB)
Audio Adapter Turtle Beach Santa Cruz
ST380023(80 GB, 7200 RPM, Serial-ATA/150)
Win2000 pro
21" Trinitron monitor...yes!

...and Doom3 or Far Cry demos stutter some.
Obviously worse as I turn up the details.
Is this about right?

UT 2003 plays smooth with detailing turned up.

[Mojambo]

1. I really don't think you should be seeing a lot of stutter

with those specs.

But I haven't really fooled around with Doom 3 much

[0rganism]

2. My first guess is "update your video card drivers"

The key here is UT2003 runs okay, but Doom3 and Far Cry do not.

It's possible that Doom3 and Far Cry are accessing your video card with newer libraries that are implemented relatively inefficiently by older drivers, whereas UT2003 is relying on a slightly older interface that is well-supported in the drivers you're using. Check the ATI site for any driver updates for your card, if you haven't already.