Wearing rings on Shabbos (Shabbos 57a)
The Mishna seems pretty clear that a woman cannot go out wearing a ring on Shabbos because she might take it off to show how beautiful it is to her friends. The Shulchan Aruch quotes this l'halacha in siman 303 seif 10. Then in seif 19, the Mechaber says that anything that is asur to be worn in reshus harabim is even asur in a chatzer with no eruv. He says that some even say that these things can't be worn in the house and certainly not in a chatzer which has an eruv. He then asks the obvious question - Why do women today just completely disregard this halacha and wear rings whereever they go.
He has a few possible suggestions why they do this:
1. Really it's not allowed but try telling that to your wife! It's better that they be shogegin and not mezidin (this is based on the Tosafos on daf 55 which says that if you know that someone won't listen then it's better not to give them musar).
2. We hold like the first opinion that the Mechaber said that it's not asur to go out to a chatzer even if it doesn't have an eruv with a ring on and nowadays we don't have too many reshus harabims d'oraysa so women wear rings in our carmelis'.
a. The Mishna Brura points out a problem with that is that when we do have a reshus harabim d'oraysa we don't tell women to take off their rings. Also, he says that we pasken like the second opinion quoted above that you can't even go out to a chatzer meureves and certainly not to a carmelis because you might come to carry it in a reshus harabim. So he says that since there are basically no reshus harabim d'oraysa there is no need for the gezeira in a karmelis.
3. The Rama adds another possible reason that nowadays rings are much more common so they're not as likely to take them off as they were in those days. Then they only wore rings for special occasions so they made the gezeira but the reason doesn't apply anymore.
I think that the problems with the first answer are obvious but there is a big chidush in the second and third answers. We are saying that batla taama batla gezeira. Just because the reason doesn't apply anymore the gezeira doesn't either. We don't always say that though. For example by tekias shofar we don't blow it on Shabbos even though you could say the same thing as the Mishna Brura says here. There aren't really many reshus harabims nowadays so according to the logic stated above we should be allowed to blow shofar on Shabbos.
Rav Hershel Shachter has explained that there are two different types of gezeiros. Some are made with the reason so the point is that once the reason no longer applies then the gezeira doesn't either. That was the situation here. The chachamim said you can't wear rings because you might come to carry them in reshus harabim. If we know that the reason doesn't apply anymore then you could wear rings. However, by shofar the reason was only stated later. There was a takana made not to blow shofar on Shabbos and then years later Rabba explained why the takana was made. The gemara wasn't even sure. They knew you couldn't do it but didn't know why. Therefore, even though the original reason for not blowing may have been because otherwise you might come to carry it, even if you know that the reason doesn't apply anymore the gezeira still lasts.