What is the best way to respond to students adding teachers to facebook? As a teacher and a teacher manager, I noticed that the students frequently ask teachers for their facebook names or send them friend requests.

I think that students having their teachers' personal lifes on the facebook feed leads to situations inside the classroom that compromises the way students see the teacher. 

How should I respond to a situation where teachers actually accept the friend requests? 

UPDATE

Thanks to @JoBedard statement about the "age factor":


  It depends on the age class of people your teaching.


We considered useful to specify that the students are age 13 to 20 years old. I would like to add that they are 90% women and from the south-american society, which has different behaviors and educational principles.
Do as with any other person you don't want to have on Facebook: ignore the request or cast a silent no (pro tip: if you configure Facebook in pirate language, it becomes "begone, ye scurvy dog!").

Most people will get the idea: you don't want them there, and will not think further. If someone insists beyond reason, use Facebook's tools to report harassment (chances are you are not the first nor the last one). For anything in between (a message saying "would you like to be friends with me?"), a polite answer saying you don't feel it is appropriate should work. 

If you are asked in real life about it you have two options:


Be direct and say "I prefer not to disclose it" or "that is personal".
If you want a more diplomatic indirect way, claim you don't use it much and change topic.