Another vote for fetchmail with the addition of procmail as the local delivery agent in Postfix. Procmail lets you write "recipes" to handle messages based on their characteristics. For instance,
Originally Posted by bytesoup
This recipe would only work if the recipient is the root user. In that case, a message from "firstname.lastname@example.org" with "reboot" in the subject line would trigger a restart.
! "/sbin/shutdown -r now"
The e-mail recipient's permissions will matter greatly if you try using a system like this to "perform some actions on the server."