I think it all depends on the nature of the break up.
I broke up with a serious psycho who gave me a diamond and saphire bracelet, and as soon as I severed those ties, I sent it back through the mail (heavily insured).
I've kept some small silver pieces, though, from my first boyfriend. They weren't expensive enough to return, and I don't wear them, but they remind me of that time in my life and how much his gifts meant to me at the time. I'm not still in love with him by any means, but I'm sentimental, and I view these pieces of jewelry as a memento of my first real relationship.
The jewelry that gets the most wear is the jewelry I've chosen for myself and gifts from my husband, who tends to know exactly what I like.