The fictional ring sought by Sauron in J.R.R. Tolkien’s The Lord of the Rings is the One Ring.
Sauron forged the One Ring in the fires of Mount Doom to control the other Rings of Power and dominate their bearers. He placed much of his own power into it, making the ring both a weapon and a vulnerability. If it is destroyed, Sauron’s power is permanently broken.
Bilbo Baggins finds the ring in The Hobbit, where it is initially treated as a useful magical ring. In The Lord of the Rings, Gandalf discovers that it is the One Ring and sends Frodo on the mission to destroy it. Frodo ultimately carries it to Mount Doom, where Gollum causes it to fall into the fire.
The One Ring is also called the Ruling Ring. It should not be confused with Narya, Nenya, or Vilya, the three Elven Rings, which have different histories and powers.