There is a draft for standardising the displaying of notifications to the user from webpages. Basically the same thing you know from e.g. your email program when you receive new messages. I think if we could make phpBB support these as an alternative / additional notification mechanism that would greatly improve working with a forum.
The draft is at http://dev.w3.org/2006/webapi/WebNotifications/publish/
It seems to currently only be implemented in Chrome and Qt Webkit but I expect that other browsers will follow soon. Obviously it would need to be entirely optional, so older browsers do not have any problems.