Social Media Genealogy you can find a wonderful PDF file with thousands of links to facebook groups dedicated to genealogy. Much of this list is location specific groups, but there are lots of others as well.
You can connect with popular genealogy websites through Facebook (e.g. Ancestry, MyHeritage, and FamilySearch). You can be in groups and like the pages of popular genealogy bloggers (e.g. GeneaBloggers, dearMYRTLE, and Cyndi's List). There are groups for various topics in genealogy. You can join groups dedicated to finding living distant cousins. And if you just want to chat with other genealogists about any- and every-thing, there are groups for that.
You can also start your own group. I am in a private group of family genealogists started by my 1st cousin once removed. We share information and photos on just our shared family line. It's been great to see the research my own family is doing and to share what I have done as well. It also helps reduce the amount of overlap in research because it's easy to share our work with one another.
How do you use Facebook to connect?