Types of Viruses
Boot sector viruses - Computer operating systems use part of the hard disk when starting up after the computer is turned on. This area of the hard disk is called the boot sector. When a virus infects the boot sector it can load itself before the operating system. When floppy disks (which also have boot sectors) were common they could be used to boot as well and were a common vector for infection.
Memory resident viruses - These viruses stay in memory, like the name suggests. Others just move from file to file and program and program.
Polymorphic viruses - These change their "shape" to make them harder for anti-virus software to detect.
Macro viruses - Many business software programs and suites have macro language and scripting features that can be converted to use for viruses.
CSS viruses - Browsers that have scripting functionality enabled can be exploited by cross-site scripting. Web sites with advertisements that come from another source (as most do) can be especially vulnerable.
Cavity viruses - These viruses hide within executable files using the "free space" within the files so that the total file size does not change and arouse suspicion.
Metamorphic viruses - these rewrite themselves each time they infect a new file.
Trojans - A trojan appears to be one type of file or program but is actually a virus.
Worms - Worms do not require user actions to spread, they move from system to system over networks on their own. For more information see my articles on computer worms, specifically the Conficker worm, and how to protect your computers and networks from them.