My biggest pet peeve about twitter right now is how little useful information they provide when you get a new follower via the notification emails.
How about "people you follow in common" or people "who follow both of you"? How about a digest of their last 10 tweets?. Some of this data you can't even get on the site.
They barely hit the minimum bar for a social network.
I've only used twitter for a few weeks, but I very quickly got to the point that I just delete the notification emails without reading them. They don't have any content at all beyond the notification that there's a new follower, about half a bit of information.
I agree with the first two suggestions. I wouldn't want anything the user could generate (like recent Tweets) to be included, otherwise it's just an easy way to spam me.
How about "people you follow in common" or people "who follow both of you"? How about a digest of their last 10 tweets?. Some of this data you can't even get on the site.
They barely hit the minimum bar for a social network.