In J.R.R. Tolkien’s The Lord of the Rings, the object that must be destroyed in Mount Doom is the One Ring.
Sauron forged the One Ring in the fires of Mount Doom during the Second Age. He placed much of his power into it so that he could dominate the other Rings of Power and control their bearers. Its destruction is therefore the only way to permanently defeat Sauron, rather than merely taking the Ring from him.
Frodo Baggins carries the Ring from the Shire toward Mordor, accompanied for much of the journey by Samwise Gamgee. At the Cracks of Doom, Frodo claims the Ring instead of voluntarily destroying it. Gollum then bites off Frodo’s finger, falls into the fire with the Ring, and unintentionally completes the quest.
The Silmarils are jewels central to Tolkien’s First Age stories. The palantíri are seeing-stones, and the Arkenstone is a precious heirloom of Erebor. None has the One Ring’s role in Sauron’s defeat.