I recently realized that it would be helpful to me (and probably other users as well) if a notification about unread answers would also show in a favicon, for example as a red circle in its top-right corner. Could you please add that?
I dislike this idea, for several reasons.
First, it will it be confusing when you have a lot of tabs open. Which tab to open? If you receive a notification on Stack Overflow, will all tabs show a notification? Also those from other sites?
Second, some browsers cache the favicon for longer times. That will show the 'unread' notification for longer than necessary... Confusing.
There is already a good way to notify of changes: the title. It shows
(1) when the question list is updated. Altering that to show notifications would be nice. Also, I like the suggestion to allow desktop notifications, as some browsers support (just like in chat).