I'm cleaning up a massively spyware infected computer belonging to someone else. Spyware is something like a virus, with a different method of spreading. It will slow your computer down, show ads that you normally wouldn't have to see, and may expose your private data to others.
There are a lot of questionable or downright fraudulent anti-spyware programs on the internet. Several good programs are:
Spybot Search and Destroy
If a program says something like "Download our free version to scan your system. If the free version finds a problem, you can use our pro version to remove it" run away. These are very likely to be scareware--The free version will detect problems even if you don't have any, and won't shut up until you pay. Research any anti-spyware or anti-virus program before installing, and never buy from a pop-up window.
You shouldn't run more than one antivirus. You probably shouldn't run more than one "real time" or "preventative" anti-spyware, but it is fine to have more than one anti-spyware installed, and to run them at different times--Some programs have different strengths.
If spyware is found and removed, reboot and scan again until either you don't find spyware or you get frustrated. Once you get frustrated, google the spyware name for removal instructions. Ignore the ones that want you to buy stuff, or stress how dangerous and difficult removal is but have an Ea$y $olution handy if you'll pay them.
If you have a particularly stubborn spyware problem, the Spybot Search and Destroy people have a malware removal forum where you can get expert help. Before you post, read the "Before you post" post at the top...They have fairly strict rules to make things as easy as possible for the volunteer experts--They don't allow random people to give advice on this forum.
This is another post where I'll take suggestions in comments.