I find this distinction to be very important. While I am very friendly with my students, and discuss all manner of subjects (both school-related and non-school-related) with them outside of class, I always politely decline any social inviations (the exception being social events that are auctioned off for charity or school organizations). I also maintain certain formalities; e.g., only using "Mr. X" or "Ms. X" to address my students, and requiring they address me as "Professor Leach."
