I always was under the impression that if the woman breaks off the engagement, she returns the ring and if the man breaks it off, the woman keeps the ring.

YES- Give back the ring. Another thought, even if you do get married and then it ends in divorce and you were given any of his family jewels (in any way shape or form) give them back as soon as the split is decided without discussion or an arguement.

I say the ring is hers to do with what she wants. He gave it to her. Should she sue him for any gifts that she bought for him during their relationship? When you give something to somebody you can't expect to ask for it back under any circumstances if you don't want a person to have what you are giving to them don't give it.

I'm with Manta. I have always believed that if HE breaks it off, it's yours. If YOU break it off, you have to give it back.

YES, I have always believed that if the wedding is called off by either party that the ring be returned either in person or by private courier obtaining the signature and full printed name of the person receiving/signing for the package.
The ONLY exception would be if the intended spouse passed away prior to the wedding, but even this depends on another factor. If you received an Heirloom piece of jewelry. Then unless the family wants you to have it, that you do return and as soon as possible.
An engagement is just a period of either pledging yourself to another or entering into a contract with the final outcome being a wedding. But if the two people involved are no longer "pledging or entering" into that contract (no matter who made the decision), then the ring belongs to the gentleman or his family.

No way. Gifts are given out of love, and not conditional. Unless it's a heirloom, it's up to the girl. I hope she's not keeping it out of spite when it's going to sit in a drawer all of her life, but if she wants to, then she can. We don't know what the conditions of their relationship and breakup were, but she does, so she's the best judge of how to handle it. If it's incredibly valuable, maybe she just wants to sell it, and I don't see why she can't. It belongs to her. If the man wants to say 'Here's a ring, but if we don't get married you can't keep it', then there are ways to legally ensure that, which I strongly advocate to avoid this kind of crap. It's sad, but these days everything in a relationship needs to be legally documented or you won't have a case.