There have been a lot of complaints about forum notifications appearing within the messaging system. Several options for resolving this were outlined at http://docs.moodle.org/en/index.php?title=Development:Forum_notifications_as_messages
To differentiate between messages and notifications we would add a "notification" column to both message and message_read. One they are read they would be moved from message to message_read as per normal. The message screen however would ignore read notifications.
This would allow email, jabber notifications to work as per normal. Popup notifications would still take the user to the messaging screen to read the notification but it would then be hidden when they return to the messaging screen in future.