In a word, "no."
Any computer that is attached to a network is not immune to viruses. But, as with everything else, it's relative. If you compare the vulnerability of Linux to Windows, you can understand why so many say Linux is immune
Sure Linux is bit secure out of box, but Linux desktop is all together different thing. It is just matter of time, once Linux got popular crackers will target Linux desktop too (think of all those net-books loaded with Linux). Right now there is not much protections for normal user account and users who will foolishly click on something in an email with attachments. However, SELinux or AppArmor may be used to protect the system.
There are 80% of people using MS (just a guess?) therefore, more hackers are working in an arena that has the most possible place for success
Even worse, Microsoft's email software is able to infect a user's computer when they do something as innocuous as read an email!
It is not a compliment to Apple or Linux or a fault of MS....just a fact....mostly, because Windows uses a registry and allows executional programs to run (exe files) the caveat is easier to use MS Windows, but easier to hack too
Sure, there are Linux viruses. But let's compare the numbers. According to Dr. Nic Peeling and Dr Julian Satchell's Analysis of the Impact of Open Source Software
"There are about 60,000 viruses known for Windows, 40 or so for the Macintosh, about 5 for commercial Unix versions, and perhaps 40 for Linux. Most of the Windows viruses are not important, but many hundreds have caused widespread damage. Two or three of the Macintosh viruses were widespread enough to be of importance. None of the Unix or Linux viruses became widespread - most were confined to the laboratory."