Viruses - A virus is a small piece of software that piggybacks on real programs. For example, a virus might attach itself to a program such as a spreadsheet program. Each time the spreadsheet program runs, the virus runs, too, and it has the chance to reproduce (by attaching to other programs) or wreak havoc.
Spyware - Is typically placed on your system by visiting websites and installing software. Typical signs that you have spyware You have a lot of popup windows when visiting the web or just logging on to your system. Your homepage has changed to a different site.You notice a major drop in system performance.  Your anti-spyware or antivirus utility stops working. You go to search for things and your search page has changed. New items appear in your favorites. In many cases there are no signs and it is running silently recording your actions.  Words of warning, though, Spyware can sometimes be integrated tightly into software that you use, and if you remove the spyware, that software may not function correctly. So be careful as to what you remove.
Worms - A worm is a small piece of software that uses computer networks and security holes to replicate itself. A copy of the worm scans the network for another machine that has a specific security hole. It copies itself to the new machine using the security hole, and then starts replicating from there, as well.