I belong to so many Facebook genealogy groups it's embarrassing! In addition to my local gen groups (including one I admin), there are the groups that help with research in specific countries, a genealogy translation group as well as a transcription group, an obituary finder group, many many good DNA groups some of which Lynda mentioned, genealogy software help groups, the list goes on!
Oh and don't forget the WikiTree Members group!
I highly recommend checking out a few groups, especially ones that might help you in areas you find more difficult in your own research.
Saying all that, I am not a fan of Facebook and rarely use it for personal reasons, but it is worth being on for the groups!