A worm is a program that has the ability to spread from one computer to another on its own using email, shared folders, and weak passwords. Worms typically propagate through the use of removable media, through a network, or via e-mail. Regardless of how the particular program self-replicates, as long as it is able to infect another computer it is classified as a worm. The vast majority of worms are malicious in intent and are being used for DDOS attacks and to steal private information. In the past, there have been some attempts of authors creating worm of good intent. These worms typically would attempt to download a patch onto the computer so they are no longer vulnerable to a particular exploit. Though the intent was good, the worm is still malware as it is performing unauthorized activity on your computer.
Well known worms are: