Since most email programs permit users to send "attachments," and these attachments can be executable programs, you need to be careful. Nevertheless, you cannot get a virus from an attachment unless you run the program by clicking on the attachment and choosing "Open".
Remember, if you tell your E-mail program to view an attachment, in many cases the associated application (such as Word) will automatically be run. If in doubt, do not view the attachment. Instead, check it first with a virus checker or just delete it.
Keep in mind, as well, that modern spreadsheet programs and word processing programs have full-featured macro languages, and that some people have written viruses that take advantage of this. For this reason, an attached spreadsheet or document could contain an executable macro program, and that program could conceivably be a virus. To prevent this, you can disable the macro language in your spreadsheet or word processing program. Be aware, though that this might disable useful features, too.
(As an alternative to disabling macros in MS Word, try Nancy McGough's tips on Avoiding MS Word Macro Viruses.)
Instead, or in addition to this, you can make sure to always use a virus checker. Again, try to only accept files from trusted sources, but take your own precautions as well.
Yahoo provides a list of available virus checkers.
You'll find examples of confirmed hoaxes, information about how to identify a hoax, and what to do when you receive a virus warning at:
http://ciac.llnl.gov/ciac/CIACHoaxes.html
Another useful Web site is the "Computer Virus Myths home page" (http://www.kumite.com/myths/) which contains descriptions of several known hoaxes. In most cases, common sense would eliminate Internet hoaxes.