Can a student be friends with a teacher?

[Kassi]

So, I am a senior in high school. My freshman year, I was put in band by accident. As it so happens, it was also this teachers first year in the school. Over the past four years, she has become someone who I trust, and who I know that I can talk to when things are difficult. I only recently confined in her how difficult my life can be sometimes (almost a year ago). Before this however, she would joke around with me, and even when we would go on field trips, she chose to hang around my friends an I instead of the adults.
When I talk to her, I have serious meaningful conversations. One several occasions she has said to me that I am one of her favorite students, and my friends (who also are in band) seem to think that I am her very favorite because we have so much in common. She has also said to me that my graduating class is special. We are the first class that she will have seen through all four years. And when I graduate in a few short months, she said she will be in tears and will miss us.
So, I already know that I am one of this teachers favorite students. And I have told her that she is by far my favorite teacher. Now, when I graduate, she will accept my friend request on Facebook. I really want to continue talking to her. In class, I understand that she is not my friend, and that she is my teacher, and her job does not require her to do certain things that she does for me. However, we are relatively close in age (7 years), and she has told me personal information about her own life too!
Would it be frowned upon to still keep in touch with her after high school, and possibly her friend?

[MerczMertz]

Not at all...go ahead!

[Sandy]

Sounds like it would be okay. No boundaries are being crossed and no one is feeling uncomfortable.

[Courtney]

I've been teaching for 7 years and had the same type of thing happen to me. Many of the dancers and students I coached graduated, requested to be my friend on FB and we keep in touch. Nothing wrong with it!