Depends how long you were married, who's at fault for end of marriage, were rings viewed as gift, who paid for rest of wedding and so on. I would just stick to bigger assets like house, car, bank accounts and stuff. You each would end up with ring you wore unless her/his ring belonged to a grandmother or something. If ring was a family gem then fight to get it back.
A spouse can ask for half of the cost of a wedding rings set in divorce; in fact, they can ask for anything. This doesn't mean they'll get what they ask for, because it could be very hard; unless the rings is very costly.