Do you friend your agent on facebook?

It depends on how you run your Facebook. Some people keep a fairly professional "voice" even there, in which case I think it would be fine to friend your agent; however, if you regularly post party pictures or in-jokes with old friends, I'd advise more caution.

Until I saw this thread, it never occurred to me to search for my agent on Facebook. But he's there.

Yep. And my editor. She wrote a congratulations on my wall when I got into college