First off, I'm NOT talking about a PBBS or mini BBS, like in the Packet Radio days. I'm thinking of something similar to what JS8CALL does, where someone can leave me a message when I'm in "away" mode.
The fact that I have a message would be indicated by some sort of button on the interface. Clicking on that button would open a window where the message could be read, and possibly replied to.
It would also nice if I could leave a message for a station that connected to me, and have them notified at connect.