Hey - I'm glad there's some other folk out there wanting Elgg notifications!
In no particular order :
1. Friend Requests
2. Activity in Groups to which you are a member (this could be simply "7 new discussions have been created in 'Staff Room'")
3. Activity on your content, eg "3 people like your comment, 4 people have commented on your blog" etc
4. Calendar Events, eg (Events this week...)
Obviously some of the above would rely some 3rd party Elgg mods (
http://community.elgg.org/pg/plugins/all/) - but the activity ones (2 and 3) could probably be undertaken as a generic approach?
I feel the stronger the integration you can make Arrowchat, the more interest I can direct your way from UK educational establishments! :D