No. Not Saruan's ring, you had to destroy it remember? But you must keep your wedding ring (if you are married)! Who haven't watch Lord Of The Rings right? Almost everyone must had watched it at least once (I thing had watched 4 times). In the the Return Of The King, Frodo had to destroy the ring in order to save human from Saruan's Dominion. But in reality, if parents were to throw away their rings, this may not bode well for their their children.
Parents read this: Not wearing a wedding ring may mean more than just a lack of commitment to the marriage. It can also mean a parental neglect to children. Alberta University social psychologists observed that young caretakers and parents who chose to discard their wedding rings were also more likely to be less committed to their children.
The observations involved a study of 862 caretaker-child combinations to measure their level of neglect. If your spouse has been keeping the ring off the finger, it's time you keep one eye on your kids as well. So parents, do keep your rings always on your finger. I'm sure your children will be glad to see it all the time. =)
P.S.: For couples, if your partner is taking off the rings that you gave...it also might indicate his/her lack of commitment. Beware!