My boyfriend paid for my plane ticket for our vacation and I told me I would pay him back.he has ended the relationship and is demanding the money for the ticket.do I have any legal rights?

Yes, the right to pay him, he paid and you told or agreed to pay him back, so why now do you wish to break the agreement.

If you had not agreed to pay him back, then you may argue it was a gift but not now.

You were going to pay him back so just do it

The way you describe it, there was an agreement that you would reimburse him. So you have both a legal and moral obligation to do so. If he can prove that you were aware that this was a loan and not a gift, he will win in court.

... and I told me I would pay him back...

What does this mean? Literally, of course, it means that you talk to yourself. I suspect a typographical error.

You told him you would pay him back? When, after or before he gave you the ticket?

I get the impression that you are hanging a lot of importance on the fact that he broke up with you.
So - why did he end the relationship?
Doing the Right Thing does hinge partly on the answer.

(As for his chances in court - I have seen this go either way on all those TV shows.)

I'm in NY - oral agreements are evidence in SC Court. You admit you said you would pay him back. What is your argument against paying him back?

You have a legal right to pay him back as you promised.