Think you'll need more than Ad-Aware, spybot travels through P2P programs such as Kazaa or MIRC, or worse, if you already have a trojan backdoor installed, according to Norton's site.
http://securityresponse.symantec.com/avcenter/venc/data/w32.spybot.worm.html
Having anti-virus is a good idea, but you might want to do a trojan scan as well, just to be safe, especially if you don't run P2P or IM apps.
As far as viruses installed, some anti-virus companies (Norton for example) tend to work on java applets that attempt to add bookmarks to your IE, change homepage, etc. A really bad one uses the .class applets, on those as long as Norton catches it you're okay.