The Rings of Power in J. R. R. Tolkien's Middle-earth legendarium are magical rings created by Sauron or by the Elves of Eregion under Sauron's tutelage. Three were intended for the Elves, Seven for Dwarves, Nine for Men, and one, the One Ring, was created by the Dark Lord Sauron himself in Mount Doom.
Sauron intended the rings to subvert these races of Middle-earth to his power, since the One Ring was the Ruling Ring that controlled the others. Sauron's plan was not completely successful, for the Elves hid their rings and did not use them while Sauron held the One, and the Dwarves' rings did not respond to the One's control as Sauron expected. But the nine mortal men who wore the Nine became the Nazgûl, Sauron's most dreaded weapons.
Tolkien's The Lord of the Rings is largely concerned with the attempt of Sauron to recover the One and the efforts of the West to forestall him by destroying it. The One is destroyed near the end of the War of the Ring when it falls into the Cracks of Doom in Mount Doom. Tolkien is not entirely clear about what happened to the other rings, though he implied that the power of any that survived came to an end. After the War of the Ring, the three Elven Rings were taken by their bearers over the sea to the Undying Lands.
Tolkien's essay "Of the Rings of Power and the Third Age" in The Silmarillion gives the background of the making of the rings. At the end of the First Age, Sauron evaded the call of the Valar to surrender, and fled to Middle-earth. Midway through the Second Age he came in disguise as Annatar ("Lord of Gifts") to the Elven smiths of Eregion, who were led by Celebrimbor, and taught them the craft of forging magic rings. Tolkien writes that the Elves made many lesser rings as essays in the craft, but eventually with Sauron's assistance they forged the Seven and the Nine. The Three were made by Celebrimbor himself without Sauron's assistance; they remained unsullied by his touch.