As a future teacher, I have to keep in mind that my public identity, which also includes my online identity, plays an important role on the perception or the impression that I give to my students, their parents or my colleagues, to name a few.
On Facebook, I have to pay attention to my posts and pictures to always remain as Joey, the professional English teacher. After knowing that everything I have posted so far on Facebook will always stay on my account, I know that I will need to create a new professional account... I think we need to make a distinction, as in real life, between our personal life and our public life. I really think it is a good thing to add your students on Facebook. You make yourself more accessible for any questions or comments they may have. You may also directly see the opinion of your students about one of your project on the net, or anything related to the school. However, make sure that your security on your personal Facebook account is maximized, so that you can share freely with your close friends and family. Be careful with what you put on the net, don't forget, you're a TEACHER!
I went on Google and did a little research with my name. I only found my Facebook account. Erase everything on the net that could give a bad impression for your professional career.
I advice you to do regularly an update of your Facebook account. Delete all the pictures that you think are not necessary. Do the same with your "friends", just keep the ones you still talk to or are in touch with.
I personally will talk about Facebook with my students. I want them to understand how to use well this incredible site. This way, I'm sure, we will share a lot in class, as at home. They and I will not feel bad to ask: "do you want to add me as one of your Facebook friends?"