Ideally, I would like to be able to add people as friends (with their approval). So that when they ask a question, I get a notification.
How is this useful?
I have to exchange e-mails with co-workers about C++ questions. And often I need to make a post on SO and send them a link. It would be more user-friendly to just add friends and avoid e-mails.
The only disadvantage of it that I see is that users will boost their friends' ratings faster than average, which makes it unfair. The advantage for the community is that more users will use SO.
One hack (or short term solution) would be to create a tag with the name of a group and all members will rss to that tag.