I'm a little surprised by the votes. What are the reasons for no?
Personally, I think if you are in a creative field (acting, writing, music, etc.), Facebook can be a great networking tool. It is a place to build out relationships with contacts from various events. In other professions, I can see why it wouldn't be as beneficial.
As for LinkedIn, I think I can echo what others are saying and state that it really hasn't been that useful for me. Not sure of its full potential though.