The term "malware" encompasses Trojans, adware, spyware, keyloggers, hijackers, dialers -- things of that ilk -- as well as viruses and worms. Malware stems from malevolent, malicious or malignant -- take your pick.
Virus attacks continue to decline. Hostile software writers have graduated to more detrimental attacks, such as Trojan-horses and spyware. The number of these kinds of attacks has increased dramatically. There's almost too many to keep track of.
Spam techniques are now being used extensively to distribute viruses and worms. Melissa, Love Bug, and MyDoom are examples where malware uses spam techniques to propagate itself after being triggered by the victim.
Some viruses are designed to broadcast spam. For example, the So Big worm installed software and then used it to relay spam.
Malware can invade your computer using one or more "attack vectors", in particular email, email attachments, evil websites and evil hackers (the "4 Ea's").
Instant messaging, IRC (Internet Relay Chat) and P2P file-sharing networks are beginning to provide new routes of attack. These Internet services rely on cozy connections between your computer and others. That makes these services handy vectors for hostile exploits. [info]
More malware gets into computers from popup windows and other Web page shenanigans these days than from email attachments. Popups advise us that we need additional software to fix a problem, properly view a page, or some such malarkey. (Yeah, like I could really read Chinese characters if they were "displayed correctly".)
Trojan horses are delivered by attachments, worms or hackers. They allow the Trojan master (or others) to control your computer remotely, including spying on you and stealing from you. Trojans are often used to attack other computers so that attacks can't be traced to the actual perpetrator.
Spyware has become the most common kind of malware after viruses. Spyware snoops while you use your computer and uses what it finds to take advantage of you in some way. Spyware is generated by various strains of "bottom-feeders" (some of them at major companies). Spyware often contains defective code, and it can bog down your computer or make it prone to crash. Keyloggers are a form of spyware. They capture and pass along your keystrokes.Adware is freeware that displays ads while you use it. It often sneaks spyware in with it.
Dialers hijack your modem and dial offshore numbers or premium services. The end result can be huge charges, which are nearly impossible to remove.
Browser hijackers set browser home pages and search settings to the perpetrator's site or to sites that are in collusion with them.
It's not very important to understand exactly what each of these categories of malware does. It's more important to keep all of it off your computer. The 7-step Plan will help you do that.
What to do if you find malware on your computer.
"Malware: what it is and how to prevent it" -- an superior article at Ars Technia on all aspects of malware
Links to more malware information on the Web.