Let me present you a well known virus for Linux : rm
Wrongly used with root rights it just delete's the whole content of your drive.
And there you got it. Linux/Mac/Unix are as safe as the person behind the keyboard.
Your browser will never run as root ,so it can never start processes as root.
Even if you browser lights up like a christmas tree , it won't get into the system ,because it's not running as root.
If you however switch your brain off, and start executing all your stuff from root, add repositories from unknown sources ,you will put yourself willingly at risk.
In this case no anti-virus scanner can protect you.
It's like asking for airbags everywhere in your car because you're going 200Mph all the time.
Just don't do it , stick to the speed limit ,and use the security that's been implemented.
HOWEVER !!! What IS advised ,is that you're using a sepeate proper proxy server with firewalls integrated that scans for bad traffic. This will protect mostly what's behind it (windows/linux/mac/etc.).
You can build this yourself with for example this distribution : ClearOS
http://www.clearfoundation.coml
The biggest security threat for the moment is social hacking , no antivirus can stop this.
But the fact that you need an antivirus or not ,depends entirely on how much stupid things you'd like to do on your OS.