Do companies use virus protection software on all UNIX servers that are used as web servers even if the servers are not used for e-mail traffic?

Has anyone installed Norton Antivirus software on their UNIX web servers or do the security patches cover viruses and worms?

No... because UNIX-like operating systems are built on a completely different architectural philosophy than Windows/DOS systems...... and UNIX-like OS are not easily exploited by viruses as are Windows/DOS systems.

The operating systems are completely different......

Well, Unix antivirus is normally only good if you're running a fileserver (like Samba) for Windows machines, or an e-mail server. If you stay up to the moment on your vendors security patches, you'll avoid most problems with worms / etc... Usually, people will begin to use security holes after a patch has been made available. Using a bit of common sense, and not running any unknown programs as a root user will prevent viruses and trojan horses, and closing off any network service that you don't absolutely need, along with properly configuring the ones you do is the key to a secure machine.