What did you do when you had a boyfriend or girlfriend who wanted to keep the relationship platonic?

I think this happens fairly often. I think people might want to keep a relationship platonic for a variety of reasons, ranging from obligations to their religion, or obligations to other people they were involved with, to wanting to not cheat to being a virgin and probably many other reasons.

Have you had this experience? Why did the person want to keep things platonic? How did you feel about that? Did you respect the reasons your partner gave? Did you keep the relationship going?