VIRUS	A computer virus is named because it behaves much like a biological virus in the real world. A Virus is not capable of reproducing its own kind and relies on the reproductive mechanisms of host cells to propagate itself. In the computer world a virus attaches itself to another program and uses that other program as the means to spread itself through the system, finding all non infected programs and attaching itself to them.
Worm	A computer worm is a program that exploits vulnerabilities within a network or operating system to gain access to that system and set up shop, where it then starts to look for other vulnerable systems that might be networked to the one it is in. By repeating this process the program "worms" it's way through networks, consuming system resources as it goes. It may also be programed to seek out and damage certain kinds of files. A worm can attack your computer without you opening an email attachment or running a program.
Trojan	This one is named after the infamous Trojan horse. Trojans are usually programs which hold themselves out as being useful tools or utilities. It might be disguised as a paint program or a game, you run it and it starts to attack your system. In Microsoft Windows it is a wise idea to change your Windows Explorer viewing preferences so that the file extensions are always visible. By doing this programs with names like "Sunset.jpg.bas" will be revealed as a Visual BASIC macro and NOT the picture it was pretending to be. In Sept of 2004 Microsoft acknowleged that their programs which decode JPG files are vulnerable to exploitation by crackers. This means it is possible to make a JPG file which can attack your machine. Patches for this vulnerability are available on the Microsoft web site. If you don't have the patch, or you don't know if you have the patch, use Windows Update to keep your system as up to date as possible.