It depends on what you do.
The pure power user
A user that sticks to the distribution provided software only, avoids fishy browser plugins such as Flash and Java, and always updates his system does not need an antivirus.
The reason is simple: an antivirus can only detect known viruses. If his system gets security updates on time, this is just as good. Because the security updates usually roll in a fast as the antivirus signatures.
The file server operator
If you are operating a file-server for Windows users, you want an Antivirus to protect the Windows users.
If you like installing third-party software from non-official package repositories "PPA"s, whatever that you cannot trust, if you manually install software that will not receive automatic security updates and just always jump the latest trends, maybe even try running windows sofware on Linux, then you are just as vulnerable as the average Windows user, who is downloading unsigned software over the internet. Get an Antivirus.
The power admin
The power admin writes his own tool that frequently computes checksum for key parts of his system and sends them off-site for comparison. Since most of the files come from official software packages, there exists a known "truth" of correct checksum. Any modification of a system file is quickly detected, but since his checksum service is not off-the-shelf but a custom solution, any attacker misses this hidden trap, and triggers the alert. (There exist off-the-shelf solutions such as tripwire, but they are fairly easy to disable.)
If the virus actually gets that far, and isn't earlier stopped by sandboxes and SELinux policies hand-crafted by the admin in minutious fine-tuning.
An anti-virus provides virtually no benefit here.