If you had a friend like this, will you get annoyed?

You don't need to tell her everything :) Talkative people can cause such problems. If she is mature enough tell her. Communication is never bad

If you want an honest answer, here goes. I tend to be very direct, and would tell her, "Look, this information I share with you is between you and me - not you, me, and your boyfriend. If you want to share something I tell you with him, could you please ask me first if I'd mind?" Something along those lines. If she gives some sort of reply like she and he share EVERYTHING you could do one of several things. Either say in that case, they can share you and you'll start calling and texting him and be his good friend, too, and tell him everything she tells you....OR - you could say, honestly - that is fine for every other area of her life except where you are concerned. If you tell someone you are not comfortable with something, and it's brushed aside, that is very inconsiderate of the person. That person is not a friend. A friend would take your feelings in to account. She can't undo what she has already done, which you could acknowledge, but you can let her know it stops here and now. And if she continues with her behavior, you are dropping the friendship. You could also ask her how she would feel if you repeated every intimate thing she told you to your boyfriend (whether or not you have one is not relevant). If she says she's cool with that, tell her you are not. If she won't stop after your request, as I said, she is not a real friend. A real friend is considerate of a friend's feelings. You don't owe her a reason, other then to say you are not comfortable with it. And you will let her know what you are comfortable with her sharing with her boyfriend. That way - you aren't telling her not to say anything - but rather, to limit what she shares to what you don't mind her sharing. You don't want personal details revealed, obviously, but if she tells him you two had lunch together or something like that, that might be okay. It's really up to you how far you want to go with this. But that is what I would do.

I'd be annoyed and would, if it were my friend, have to talk to her about it as by doing that she's (your friend this time) betraying your confidence.

Well I don't know if I would be friends much longer with people who cannot keep a secret. Or very least, not say anything that I would never want to get spread around to anyone else. Of course, that is just a good practice, to never say anything that I don't really want anyone to really say. Secrets are only kept by two people if one is mute. Of course, really secrets are just something that are utterly tempted to tell. When someone tries to tell me a secret, I shush them. I shouldn't really be told with them, for their own good. It is just something that there are tantalizing bits, juicy, right on my lips and I'm so tempted. It is a temptation to really say a lot of things. Hence why I don't tell others.

A good analogy about the snake; watch out. God warned Eve. Eve didn't listen. As for the whole gossipy saga, women often tell their secrets to their mates because in the woman's euphoria she is not thinking with her head, and thinks if she tells him her secrets that they will be closer. They want to test the man, they want to hear words of love and making him a confidante in the mistaken belief that the knowledge of secrets bind people together. As for the girlfriend who shows the pictures of you and someone else, she is looking to take your man. Watch out. She is the snake. Keep your boyfriend news private by not talking about him, and tell your friend to take a hike.