You don't want to run more than one anti-virus program as they can create issues with one another. However, you can run multiple spyware programs without issue. It is actually beneficial to run multiple programs as one can catch issues another might miss. Three that I use are:
AVG Anti-Spyware
http://free.grisoft.com/doc/download...yware/us/frt/0
Spybot Search & Destroy
http://www.safer-networking.org/en/spybotsd/index.html
Ad-Aware
http://www.lavasoftusa.com/products/ad_aware_free.php
One other item to consider is rootkits. I use:
AVG Anti-Rootkit Free
http://free.grisoft.com/doc/39798/us/frt/0