Hi, everyone - 
This happened to me all the time when I was teaching and when I was
doing home visits. Some of the positive repercussions were being seen as
a "real" person and part of the community; some of the negative were
knowing more about students than was necessary or desired, having my
off-time taken up by spur of the moment work conversations, feeling like
I had no privacy, and sometimes having to make personal disclosures
before I was ready to make them (for example, they see me out with my
girlfriend when I haven't come out to the class). 

I found the best response was a friendly greeting, and if an attempt was
made for a further conversation, I would say, "I really want to talk
with you about that; could we talk before our next class?" 

Respectfully, 
Karen