There are a bunch of semi-useful professional networking sites that I use to potentially share/collaborate. I haven’t found them as useful as I would have hoped but that relates to how active one chooses to be!).
Linked in is the most common but there are other ones that are more directed at academia. I recently started a profile in academia.edu. I like the notices of people viewing my work or looking me up–particularly internationally. Other ones I use as a scientist are Nature and Science network sites.
I would never use facebook professionally even though I realize that most people do. I try to direct students etc towards one of the above to stay in touch–particularly linked in b/c it is the best known.