Note that we have a lot of articles on free antivirus protection and free spyware protection. There's no sense in going into too much detail here. Just know that there are plenty of free programs that give full access to their removal tools for free. AVG Free is a personal favorite. Avast is a good antivirus program too. Avira has a very good realtime shield. Spybot Search & Destroy is still a good program for eliminating spyware on your computer and their immunization program is fairly nice.
If you're using Firefox, then NoScript is a great add-on to prevent infections in the first place. If you just want a good removal tool, then MalwareBytes is a great program with a really well proven track record for new infections.
There are also plenty of free online virus scanners. I haven't played around with those much, but they should be an option for anyone afraid that an infection slipped through and contaminated their existing antivirus software (The scanner isn't on your machine so it shouldn't be affected by existing malware).
Finally, established programs like McAfee, Norton and new favorite Kaspersky all offer a full security suite (with extras like email protection and identity theft protection alongside their scanners).
If you're running one of the free ones, then you're probably fine.
Note that we try to stay up-to-date on new infections. If you have a specific infection that you're having trouble eliminating, then just search for the name here to see if we have a guide ready.