I found that mail such as Logwatch on a Debian server was getting sent from "root@debian", which caused Gmail to sweet it all into the Spam folder.
I fixed this by editing /etc/email-addresses:
➜ ~ cat /etc/email-addresses # This is /etc/email-addresses. It is part of the exim package # # This file contains email addresses to use for outgoing mail. Any local # part not in here will be qualified by the system domain as normal. # # It should contain lines of the form: # #user: firstname.lastname@example.org #otheruser: email@example.com root: firstname.lastname@example.org