I have a shell account on a Redhat 9 machine. I am *constantly* getting the following message:

"You have mail in /var/mail/username"

When I get new mail, it says "You have new mail in..." which is useful. But for heavens sake, I don't need to know I have mail unless it is new. I keep my mail on the server because I access it with Thunderbird (pop3) from several different computers. Is there a way to get rid of this notification? It would be nice if I still was notified when I got new mail, but if I have to get rid of that to get rid of the other that is fine.

You need to set the following variable in bash:
export MAILCHECK="NO"

There is more information in the bash manpage:
man bash