I was recently reading The Republic, by Plato, and when we came to the section about the ring of Gyges, my teacher claimed that this was the inspiration for the One Ring. I doubt he had any real evidence for this, but the story, or at least some aspects of it, are remarkably similar, so I get where he got the idea. Here's Plato's story:
According to the tradition, Gyges was a shepherd in the service of the king of Lydia; there was a great storm, and an earthquake made an opening in the earth at the place where he was feeding his flock. Amazed at the sight, he descended into the opening, where, among other marvels, he beheld a hollow brazen horse, having doors, at which he stooping and looking in saw a dead body of stature, as appeared to him, more than human, and having nothing on but a gold ring; this he took from the finger of the dead and reascended. Now the shepherds met together, according to custom, that they might send their monthly report about the flocks to the king; into their assembly he came having the ring on his finger, and as he was sitting among them he chanced to turn the collet of the ring inside his hand, when instantly he became invisible to the rest of the company and they began to speak of him as if he were no longer present. He was astonished at this, and again touching the ring he turned the collet outwards and reappeared; he made several trials of the ring, and always with the same result-when he turned the collet inwards he became invisible, when outwards he reappeared. Whereupon he contrived to be chosen one of the messengers who were sent to the court; where as soon as he arrived he seduced the queen, and with her help conspired against the king and slew him, and took the kingdom.
The story is being told by a character who is trying to prove that people are naturally evil, and given the opportunity (a magic ring that allows one to do whatever they like without being caught) people will act evil. To put that another way: power makes people evil.
We see that both rings are invisibility rings, seem to have evil origins, and both cause evil.
I wouldn't be the least bit surprised if Tolkien had read The Republic, probably in the original Greek, knowing him.
However, I also know that, at least, this wasn't Tolkien's original inspiration. The ring wasn't even faintly evil in the first version of The Hobbit, published in 1937. In 1951 he changed it so that it worked better with The Lord of the Rings, which he was working on at the time.
So the question is: Was Tolkien inspired by the Ring of Gyges, or did he come up with a similar artifact on his own?
Disclaimer: I know that I'm generalizing a bit about the nature of the One Ring, and this is a loose analysis, so don't cite me as some sort of Plato expert. Also, please do not insult my teacher.