Getting banned from Facebook is possible through a variety of ways. Impersonating Mark Zuckerberg, using a false name or posting copyrighted content are ways to get a Facebook account banned.
Impersonating another user on Facebook is considered identity fraud and is a fast way to get an account banned. For a more serious offense, organizing hack attempts on other users, corporations or websites is also unacceptable. Another thing that gets an account banned quickly is pretending to be over 13, as Facebook takes laws relating to children seriously. Posting copyrighted material, obscene content and spam in general are all ban-worthy offenses.
Lauren Ferrari was banned from Facebook after posting what to her seemed a humorous photo of her child nursing her younger sibling. The image and resulting backlash sparked a controversy, and her account was restored after a short period.
Another offense that results in banning is using any sort of third-party script to browse or view the contents of Facebook. This is for security reasons as well as to cut back on spam posts. Finally, being too social isn't accepted either, as adding too many friends too quickly results in an account being banned under the suspicion of being a spammer.