Angus gives an excellent overview of how to get up and running with Watir, a open source testing utility. Watir is basically about automating web browsers in order to help test web sites.
This is something we've been struggling with at Elcom. Like most web companies we end up having to do a lot of manual testing of sites, because it is so difficult to automate.
There's a few offerings out there (some are ridiculously priced - hello Mercury!) but nothing that really gives you confidence and coverage (in the way that say unit tests do for non UI code).
I'm very keen to hear suggestions from other companies about how you automate your UI testing.