In general spyware is not a problem in Linux, so there aren't really equivalents for spybot or adaware. Basically, Linux functions more securely than Windows, and as long as you're not running as root, it is very difficult for these programs to install themselves. Particularly since Linux doesn't have crap like ActiveX. Now this isn't to say that you don't need to take some basic security measures in Linux because there are problems lurking out there, it is just harder for them to get installed. Turn off unneeded services. Never, ever, EVER access the Internet from root. Turn on the firewall.
If you really want to dig into Linux security, I can't think of a better place to start than here