Some companies ask for your Facebook password when they hire you.
I would refuse, not only because I disagree with that on so many levels, but because in my area of specialization the protection of personal/security information (like passwords) is important, and I think that a company which asks me for my information and which hires people willing to give it up is one with a culture in which it would be impossible for me to do my job well.
That said, many people make the mistake of friending coworkers on facebook and not managing their lists properly. Even if you don't get fired for something you say or post on Facebook, if your coworkers can end up with more information than you would like and you are not in control of how they share it and or how it effects their perception of you. If there are photos of you out drinking the night before you called in sick, or if you post a complaint about that "horrid manager" you have, or that you hate your job, if anyone you work with has access to that information you can expect it to change the way they see you and they way they work with you, whether they are in charge of your hiring and firing or not.
It need not even be work related. I don't generally discuss my sex life, my politics or my (lack of) religious belief at work, not only because it is inappropriate, but because I assume that many people would change their views of me based on this information. You may not fire me because I am an Atheist, but research shows you will trust me less, and I don't need that perception coloring my performance reviews or the opportunities I am given. I do post things about my beliefs publicly on G+, but I am able to easily filter my more "objectionable" so that it is only shown to those I want to share it with. I found that Facebook was constantly resetting their system, so that even after spending hours sorting lists and carefully assigning permissions, people could access information I didn't want them to. Also, Facebook requires your to actively moderate your own page. That is if you "write on my wall" it is by default visible to everyone, this means that even if I am not using the site, people could post things which "out" me to others.