I'm going to just ignore the off-topic posts above, but in response to your post johnj, have you asked yourself why it's so important to you how many partners she has had, and why you're finding yourself so upset with her unwillingness to tell you? Are you upset because you perceive your girlfriend to be less pure? Do you worry that if she's had more partners, you can't trust her as much (and if so, why is that?) Are you concerned about diseases? Are you upset because she's withholding information from you? What information do you feel you have a right to know about her past, and why? Also, I'm curious, why do you suspect that she has had multiple partners? Is it due to something physical you've observed, or something she may have unwittingly alluded to in casual conversation? These are things that you need to ask yourself, if you haven't already.
Your girlfriend is probably reacting so defensively because she doesn't understand why her sexual history is so important to you, and she may be afraid that you might value her less if she's had multiple partners. It's your responsibility to first clarify this issue to yourself, so that you can better explain it to your girlfriend. Then maybe you will have a better chance at having a constructive, open conversation instead of repetitive, circular fights that shut down real communication.
It might also help to ask her (without accusing or assuming anything) to clarify her own position. Why doesn't she want to tell you? Is she afraid you'll leave her? How does she feel when you ask her about her past, and does she understand why she feels this way? Does she feel that her privacy is being invaded? It's important to make sure your tone, body language, and facial expressions don't convey a sense that you're blaming or accusing her. Make it clear that you're asking in order to better understand her, not to lead her into saying something that will get her "in trouble." Maybe try to talk about this when you're both calm, and if it gets too intense, you can give yourselves time to cool off before picking up where you left off in the conversation.
One thing I would advise, is that you'll get a lot further with your conversations about this if you don't write off her reaction as "hysterical". I'm guessing you wouldn't appreciate your girlfriend dismissing your very real emotions as hysterical, irrational, or unwarranted. So she would probably appreciate if you'd take her emotions seriously, even if you're having a hard time understanding where she's coming from. She's allowed to feel angry, resentful, or defensive just as much as you are.
In the end, she has a right to withhold any information from you that she wants. You can't make her tell you, but you can make clear statements about your own feelings and about why this issue is so important to you. When I say to make clear statements about yourself, I do not mean "You make me feel angry," (she's not responsible for your emotions), I mean something more like "I feel angry when you (fill in the blank) because (explain why without blaming her for your emotion)." She may never actually tell you, and you have to decide if you can live with that or not. It's not fair to either of you if you can't stay in the relationship without harboring resentment.
One last thing. If you are concerned about sexually transmitted diseases (and no matter how much she tries to write off this concern as irrational or paranoid, it is a valid concern), you have a right to ask her to get tested if she hasn't already. She also has a right to refuse, and it's up to you to decide whether or not you can live with that. It is your responsibility to take care of your own health.
I hope you can both work this out, please do come back and post with any updates (Try not to let the off-topic posts scare you off).