Apart from the One, there were also nineteen other Rings of Power. Three of them belonged to elves, seven to to dwarves and nine to men.
The elven Rings have never been touched by Sauron, as Celebrimbor forged them alone. Nevertheless, they were also ruled by the One. By Sauron's first defeat, their owners did not use their power openly in order not to draw Dark Lord's attention.
Vilya, the first and the mightiest of them, was the Ring of Air. It was made of gold with the saphire in the middle. The Ring was firstly held by Gil-galad, then by Elrond - the Lord of Imladris. The next one was Nenya - the Ring of Water, owned by Galadriel from the Lorien forest. Made of rare metal mithril, it also contained the diamond. The third was named Narya - the Ring of Fire. The ruby was its stone. The jewel changed the bearer once. At first, it was in the possesion of Cirdan the Shipwright, but later he turned the Ring over secretly to Mithrandir (Gandalf). It was revealed only when the wizard was about to sail away to the West.
The dwarves appeared to be hardened to Sauron's magic (the Seven moved them only to greed of gold and jewels), so he decided to get back the Rings with which they had been entrusted before. However, he managed to take over only three of them, because the others had been destroyed by dragons.
History of only one dwarven Ring is well known. Sauron did not participate in its creation. The Ring was given to Durin III, the King of Khazad-dum (Moria), directly from Celebrimbor. It remained in the house for thousands of years, when it was inherited by Thror, King under the Mountain. After Smaug destroyed Erebor, Thror turned the Ring over to his son Thrain, who later lived in exile. When Sauron's servants captured Thrain, the Ring was lost - the ruler of Mordor took it over.
Only the men entirely fell into line with Sauron. They became his most loyal servants - the Nazgul, or the Ringwraiths.
Only two Nazgul are known by name. The first is Sorcerer, their leader, the Lord of Morgul. During the III Age he founded a realm in Angmar, from where he made incursions into Arnor. He died during the Battle of the Pelennor Fields, slain by Rohan woman Eowyn and hobbit Meriadoc Brandybuck. The other Nazgul is Khamul - Black Easterling, named also the Shadow of the East. He was the second after the leader. Undoubtely the Rings were also given to some Numenoreans.