What can I do to protect myself from computer viruses and Trojans?

These days, practically everyone's online, downloading and exchanging files, and developers are in such a hurry to get their Web sites up or their files out that checking for a nasty bug is more of a courtesy than a requirement. If you're not careful, your computer can end up with a nasty virus that makes your files act oddly, crashes your computer, pops up bizarre messages, or worst of all, destroys your operating system.