For those who may include your LDS (Mormon) beliefs on your Facebook profile, there is an (unofficial) LDS application available. The More Good blog explains some of it here.
The app “includes space for noting your personal scripture faves, and incorporates a few scripture mastery games. You have the option as to whether or not to include the information on your personal profile.”
The More Good blog post also mentions the Ensign magazine page on Facebook, which is an official Facebook page of The Church of Jesus Christ of Latter-day Saints. The Ensign is a monthly magazine for adults. (You can read the Ensign online here.)
Other official Church Facebook pages include the following:
The New Era — magazine for youth (read online, and find other resources for youth here)
The Friend — magazine for children (read online, and find games and activities for children here)
The Liahona — international magazine (the print version comes in various languages)
LDS Newsroom (also on Twitter)