I sleep on the right, and on my right side (facing the outside of the bed). This has only been a problem when I was sleeping with someone who felt I was "rejecting" them by turning my back to them to sleep. (And no, I did _not_ just do the deed and then roll over to go to sleep. I spent plenty of time cuddling.) This has happened with a few different people, who didn't work out in the end. I have to say, I felt their need to always sleep facing each other was needy and manipulative. I don't like people breathing in my face all night, and my spine didn't appreciate it either (I have to turn over a couple of times during the night).
