I use AVG for antivirus, and I also have Spybot S&D and ad-aware.
I also have PeerGuardian. However, I have to disable PeerGuardian every time I patch UO and occasionally when patching WoW. Evidently, some of the patch servers have gotten blacklisted.
You really have to look to find the link to the free edition of AVG, they don't advertise that you can still get it free, but it's worth the trouble finding the page with the free version on it.
Another great free utility that I use is WhatsRunning. Just go to the startup section and remove all the stuff that you don't want to run at startup. You would be surprised how much better your computer will run UO after you get rid of all the startup programs that you don't use over once every couple of months. Practically every piece of software known to man thinks it's important enough to take up memory waiting for you to use it. Also, some spyware and adware programs will stick themselves into your startup. It's a good idea to check it every few weeks. WhatsRunning can do a LOT more, too, if you happen to be technically minded.
If you're running XP, you can get a 30-use free trial of Tweak-XP. It's a great optimization program; you will probably never use it 30 times; once you have used it to optimize your system, you will probably not use it more than once every 3 months or so. Just make sure that you don't have the "start with Windows" box checked, and that free trial will last as long as your computer does. I can't stand Vista; when I bought my new computer, I immediately erased it and installed XP, so I don't know if there is a Vista or Windows 7 version.
I've never used Avast, so I have no opinion about it. But all that I've heard about it is good; everybody who tries it evidently likes it.
On the other hand, I don't trust Microsoft's ability to keep my computer virus-free; the MS programming team is both as fast and successful at fixing bugs and exploits as the UO Dev team. Also, it doesn't like Firefox.
One last bit of security info: I use Firefox with AdBlock Plus, BetterPrivacy and the AVG security toolbar.