I have accepted the friend request of one former student only and for special circumstances. He was one of my late son's best friends and is organizing a memorial bowling tournament for my son's Memorial Scholarship Fund. I made it clear to him that I would not be chatting with him for reasons other than that. I am friends with his mother also.
I think you have to be REALLY careful about allowing a current or even former student in. Remember, they can see everything that is posted on your page by you and by others. I can honestly say that I don't post anything that I am ashamed of, but I can't control what others post.