Geoff Kuenning, an assistant professor of computer science at Harvey Mudd College, explains:
You can absolutely get a virus from opening just a "regular" e-mail--if your mail reader supports attachments.
Attachments are an extension to old-fashioned plain-text e-mail. The idea is to allow all sorts of files to be transferred without going through the hassle of downloading them separately. In the bad old (or good old) days, computer users had to send "pointers" to things. For example, you might tell somebody to look at a certain Web page to see a funny picture. Attachments save us from that nuisance.
If your mail reader supports attachments, the downloading is done automatically. Depending on your reader and your preferences, you may have to explicitly ask that an attachment be decoded and opened; this method is inconvenient but safer. Some mail readers will decode and even execute attached files as soon as you open the message, or even when you simply list the messages that are in your inbox. Microsoft Outlook is notorious for this kind of behavior. If the message is malicious, you will find your computer infected by a virus.
You can reduce the chance of this happening by setting your mail reader so that it never opens attachments automatically, and by never opening an attachment that you weren't expecting to get. Nowadays, it isn't even safe to open attachments from your best friend, because some viruses masquerade as people you know. You might think you are going to see Fred's pictures of his party, and actually wind up infecting your computer.
Answer originally posted September 9, 2002.