I'm torn if face-to-face interactions help significantly. Although, if I see someone enough in an unstructured way, I'll either become good friends or want to not see each other again. :)
Facebook is great for keeping in touch in a casual way. Ask questions here and there, comment on their life achievements, etc.
I've noticed that once I got more of my professional network on Facebook, I've been more conscious about posting drama, this-is-how-it-should-be opinions, etc. That's a good thing but man was it hard at the beginning to keep myself from posting rants!!! :D
For myself, it would be hard for me to say I know them, let alone call them up. Maybe the lesson for myself is that most people are pretty receptive of just being called up if you have a legitimate reason and there's no harm in being more open about connecting (you won't get in trouble for calling someone a friend even though they are definition an acquaintance).