It is no surprise that FamilySearch has moved onto Facebook in a big way since nearly everyone online now has some sort of Facebook presence. Here is a short list of some of the current offerings, bear in mind, these are all on Facebook:
FamilySearch Wiki: Since I am so heavily involved in the Research Wiki, it decided to start with this site. Obviously, this type of Facebook page does not have the usual trivial postings about daily events, but it does give information and communicate about the Wiki. This page is turning into an alternative support page. In a recent review of the page, there were posts about new resources in Canada, Louisiana, and Belgium as well as posts asking for help with indexing. Several contributors gave links to other resources.
FamilySearch (main site): This is main site on Facebook and is mostly a link to other pages. There is also another page for FamilySearch with a lot more comments on it but it is not supported by FamilySearch. This points out one of the many problems with Facebook, the lack of identities. The second page cited has no background info and there is no way to tell who put the page online. It is interesting that both the "official" Facebook page has content and comments as well as the unofficial page. The official page also has a lot of identifying information. You might want to make sure you are on an official page before assuming you are talking to FamilySearch.
FamilySearch Indexing: The Facebook page has links to Project Status Updates, Discussion Boards, Polls, Notes and Photos. It also has links to many of the pages available in the regular program.
Family History Library: This page doesn't see much activity but is a good resource for current programs at the Salt Lake FamilySearch Family History Library.
RootsTech: This national conference held in February in Salt Lake City has its own Facebook page. This page still deals with the 2011 Conference and hasn't been updated to the 2012 Conference yet.
There are a couple of pages by individuals that feature FamilySearch that I found, but if you see more than I do, let me know.