In The Lord of the Rings: The Return of the King, the One Ring is destroyed in Mount Doom.
Mount Doom is the volcanic mountain in Mordor where Sauron forged the One Ring. Because the Ring can be unmade only in the fire where it was created, Frodo and Sam must reach its Cracks of Doom.
The mountain is the final destination of the quest. Frodo reaches the interior with Sam’s help, and the Ring is ultimately destroyed after Gollum takes it from Frodo and falls into the fire.
Mount Doom is different from Mount Mindolluin, the mountain beside Minas Tirith. It is also not the same as Mount Caradhras, the mountain pass that hinders the Fellowship earlier in the story.