I'm currently student teaching (High School) and there are a lot of reasons not to friend students on Facebook. My current primary reason as a student teacher is that I'm still exploring the limits of personal information / stories that can safely be shared without it coming back as an attempted torture device. I told students I took French in high school and college and a student decided calling me "Frenchie" would be a good idea. I just laughed and said "Say 'chowder'' which defused that right away. Facebook is an unfiltered place to express myself and communicate with friends. The more people you let in the more professional you have to be which is lame. That's not what Facebook is for. Even if the students you friend are responsible with the information during class, they may share stories with other students who are not. Then you get rumors and all kinds of fun stuff. And frankly, I just don't care to keep my Facebook profile PG for the kiddies. I'm an adult that has adult conversations and adult interests.
There are professional channels to use to communicate with students and I don't have a problem talking to students in class about non-class related things. But, it's at my discretion and off the record.
But yes, I agree you should get to know your students. Some of the problem of not knowing them is large class sizes. In my three classes with 15 students each I recognize them all and know their names. In the two classes with nearly 40 students each, I'm still learning names and faces.