And yet it is.
Here's the short version of the answer: No. If you simply never run untrusted executables while logged in as the root user (or equivalent), all the "virus checkers" in the world will be at best superfluous; at worst, downright harmful. "Hostile" executables (including viruses) are almost unfindable in the Linux world — and no real threat to it — because they lack root-user authority, and because Linux admins are seldom stupid enough to run untrusted executables as root, and because Linux users' sources for privileged executables enjoy paranoid-grade scrutiny (such that any unauthorised changes would be detected and remedied).
Here's the long version: Still no. Any program on a Linux box, viruses included, can only do what the user who ran it can do. Real users aren't allowed to hurt the system (only the root user can), so neither can programs they run.
Because of the distinction between privileged (root-run) processes and user-owned processes, a "hostile" executable that a non-root user receives (or creates) and then executes (runs) cannot "infect" or otherwise manipulate the system as a whole. Just as you can delete only your own files (i.e., those you have "write" permission to), executables you run cannot affect other users' (or root's) files. Therefore, although you can create (or retrieve), and then run, a virus, worm, trojan horse, etc., it can't do much. Unless you do so as "root". Which it's simple to avoid doing.
Edited version of http://linuxmafia.com/Labels: anti-virus for linux