I just got a friend request from a student. He's not failing or anything--though the last time a student friended me, he was totally flunking--but I didn't recognize the kid's profile picture, or the kid's name right away (I do have 200 students, okay?), and had to check my class roster in order to confirm the "student" hypothesis.
The first time this happened, I drafted a long email explaining why I thought maintaining a certain professional distance was important and stuff, but then I ended up not sending it and just ignoring the request. Since then, "operation ignore" has been my basic strategy for handing students on Facebook. What do other people do?