When I sit down to clean adware and spyware off of a computer, this is usually the second program I run. Like Ad-Aware, SpyBot: Search and Destroy is a very comprehensive search and clean program, but it works in a different way than Ad-Aware does, so it finds stuff that Ad-Aware doesn't, and vice-versa.
I would not recommend running this scan while the Ad-Aware is also scanning. Run one first, then the other. But I do recommend using both programs.
One of the nice things about Spybot: Search and Destroy is it has an "immunize" feature that will help block some adware and spyware from coming into your system to begin with. It isn't foolproof, and it isn't as good as Spyware Blaster, but it does help.
And I would say this is one of the programs that you need. This program is free for home use, not for business use.
Spybot: Search and Destroy runs on Windows.