First, if the bride was who ended the engagement, she absolutely needs to return the ring. This also applies if the ring is an heirloom or stone from the groom's family. However, the waters grow murkier if the groom broke off the engagement, or if it was a mutual decision. Ultimately, keeping a ring often feels petty. The bride will often not wear it for long after the engagement, as it is just a painful reminder of the failed relationship. And after she moves on with someone else, it's not like she can wear it then. Eventually, it ends up sold or in the bottom corner of a jewelry box, next to class rings and best friends lockets from the 5th grade.
However, an engagement ring is really a symbol of a commitment that the two of you made to each other. It is a gift, and particularly if he cancelled the engagement, you are under no social obligation to return it.
Some states have different legal requirements when it comes to returning the ring, as a part of any joint property. Make sure you are aware of any ramifications of keeping it or returning it.