I asked my boyfriend if he had sex with his ex girlfriend which I know. And he said that he does not kiss and tell. And I just freaked out and hung up the phone. Should I apologize?

As this is his past it really has very little to do with you.
Yes, you should apologise for prying.

You apologize for over reacting, but the question is legit, and so was his answer. He may accept, your apology, he may not.

Man, I'd be asking myself if I even had a boyfriend to call back and apologize to after doing that.

You have to be fair about asking a question like that. If you ask, you have to assume the worst of what you might not want to hear. If you ask him a personal question like that, you shouldn't react negatively... he'll be much less likely to share personal things with you in the future.

I hope you still have a boyfriend after that episode.

I hope so too. LOL

Yes, if you are asking it means that if the answer is yes it will probably accept you, better to practice the don't ask don't tell policy for the sake of the relationship. Anything that happened before you two got together is none of your business, neither is it important.

If you're asking if he had sex with his ex in your PRESENT relationship - yeah it's reasonable.
But if you're prying into what he did when you weren't a couple - it's none of your business and he was within his rights to say he doesn't kiss and tell.

It's not important what happened before your relationship - what is important is what is happening in the present and your choices now --- best to apologize!

Have a chat with him also, do not try to avoid what happened, talk about it. You can apologize. Forget about the "past", it is only a memory. Focus on NOW and what you want to do next. Sometimes it is better not to know anything of the past.