Nineteen Rings of Power were given to Elves, Dwarves, and Men in Tolkien’s Ring-lore.
The distribution is three rings for the Elves, seven for the Dwarves, and nine for mortal Men. These nineteen rings were made before the One Ring, which Sauron forged in secret in the fires of Mount Doom to dominate the others. The One Ring therefore brings the total of the principal Rings of Power to twenty.
The Elven rings were the Three, the Dwarven rings were the Seven, and the rings associated with Men were the Nine. Tolkien’s texts do not present all of the individual lesser rings as part of this same numbered distribution; the nineteenth-century-style summary refers specifically to the rings named in the famous verse.
The number is sometimes mistakenly given as twenty because people include the One Ring. That is a different counting choice. The question’s distribution among the three peoples totals three plus seven plus nine, or nineteen.