When thinking of what kind of apps to make for social networks, thinking about what people do in their everyday life can be a great source of ideas. A big part of social networks is mapping out real connections. The concept of "Social Graph" is so well-known as to become even a bit nauseating to think about one bit more, but there are other connections besides just friendships, not all of which are necessarily mapped out yet. For some, it probably makes no sense to map them.
A person has...
a name (Name Analyzer -- at least I thought about this one!) both official and nicknames (Nickname)
age (Birthday Calendar -- still kicking myself for not thinking about this first)
x,y,z location at each time they existed -> birthplace, countries they visited (Places I've Been), grave
photons disturbed by them (Photos/posting of videos)
likes/dislikes about food, movies, music, smells, colors...
personality (Compare People)
knowledge (Who Has The Biggest Brain, Scrabble, Geo Challenge)
medical conditions, sleep cycle, height, weight, dna (a bit too costly to compare your DNA with friends, but we'll get there ;) )
ownership of physical/virtual items (can own a car, a house, stocks, money, music recordings, WoW gold...)
relationships with humans -- idols, friendships, relatives, enemies, employees/employers
- other people (Hot or Not, Compare People)
- what is wrong and right
- which gods if any exist
"Groups" by Facebook is very much a meta-application in that almost anything can be expressed as a group. It may be that applications that can add value beyond what a membership to a group could offer will be successful. One other app I'm kicking myself for not coming up with is Bumper Sticker, which solves the meta-problem that groups solves, but in a more visual way. If there is any other uninvented angle than Groups and Bumper Sticker to this, it will be huge. Other thing to think about is whether there would be value in aggregating the connections of your friends in some way. For example you have an age, and while that in itself might make a great app (Brain Age), aggregating friends' ages also gives one (Birthday Calendar).
If you can think of any other general sources of ideas, please post some. I'm sure there are still a few d'uh-obvious ideas out there to be discovered!