The term "malware" is short for malicious software and is usually used as a catch-all term to refer to any software that causes damage to a computer, server, or computer network. Some of the most common types of malware are listed below.
Self-replicating malware requiring a host file that depends on human action to spread it.
Self-contained malware, needing no host file, that spreads automatically through networks.
An apparently useful and innocent application containing a hidden malicious program.
A rootkit isn't always malware, but is technology often used by malicious programs to hide and convince the operating system that it isn't there.
A program that secretly monitors your online activity and sends the data back to the programmer.
While not in itself malware, a botnet is a giant network of "zombie computers" that can be used to carry out the instructions of the botnet owner. Botnets are often "rented" to scammers and hackers and can be used for everything from sending spam to attacking foreign governments. During 2010,more than 2 million computers in the United States alone were found to be part of a botnet.
Ars Technica has an excellent article outlining the various types of malicious software.
Antivirus Ware provides independent reviews of the best-known antivirus software products available for consumer use. In addition, their Avoiding Viruses and More page provides several easy tips on keeping malware off your computer in the first place.