I asked myself the same question not long ago and this is what I have learned:

1) If you use Linux and only Linux, an anti-virus package is not
important. It is generally considered a waste of resources and
bandwidth to scan Linux email and documents for virusses - it just
does not happen in practice.

2) But, if you receive email from Windows users and forward the same
message to other Windoze users, you might not realize that there is an
unwelcome payload attached to that message. Even though I am 100%
Linux, there is still an element of humiliation when a Windows user
tells me that the email I forwarded to them contained a rootkit in the
attachment. Subsequent to this experience I now also use a Linux
Anti-Virus package (AVG Free).

3) Also, if you should run a mail server on a linux box where Windows
users connect to, it is advisable to run a server-level Virus
protection for the benefit of the Windows users as well as to try and
reduce your mail traffic in not sending on virusses into the world in
the first place.

4) On Linux I also occasionally use QEMU as well as Wine in which I
occasionally run Windows programs. Both environments, but especially
WIndows XP within QEMU is not immune to virus infections. In theory
at least, since have not actually had problems. In these instances a
Linux anti-virus package might not help in any case.

I have no idea to what extent Wine or programs running under Wine can
get clobbered by Windows Virii, but maybe someone on this list would
know.