For people who are purely my patients, I absolutely never accept friend requests. I have a few patients who are a little more fuzzy---for example, the parents of my daughter's preschool friends--who are my Facebook friends. But I make sure to not look at their Facebook pages and they really don't interact on mine other than to "like" pictures of my kids. I'm in a fairly tight knit community and run the free clinic at a local church...I also care for many of the community pastors and their families in my practice and it would be kind of weird for me to refuse to friend them.
But I agree to be VERY careful. I refuse all other friend requests.