It's a very old tradition going back centuries, not all rings associated with magic have a stone. I have said it once, I will say it again, people thee days focus on crystals and forget about the inherent magical properties of the different metals. Many rings simply had a specific metal and then engraved design in the centre.
Some of the more famous ones which come to mind ar the ring of Solomon which features heavily in the "Key of Solomon" grimoire and also within the Enochian system of Dee and Kelley who received a different design.
Before this more medieval magic of course you also had rings in the form of talismans which would have certain metals, stones, engravings etc. and charged with influence.
In terms of rings used in ritual, it does seem to be a popular piece of equipment for many modern occultists, personally, I am a minimalist and don't use one, other people do. The power contained therein is up to the individual user and whether they have charged the ring to have inherent power or the power comes from their belief in the rings use is not only up to the individual practitioner, but also one's beliefs regarding magic and how it works.