The One Ring is destroyed in the year 3019 of the Third Age. Frodo carries it across Mordor to Mount Doom, the volcano where Sauron originally forged it, because only its own place of creation can destroy it.
At the Cracks of Doom, Frodo finally claims the Ring instead of casting it away. Gollum attacks him, bites off his finger, and falls into the fire while clutching the Ring. Its destruction breaks Sauron’s power, causes Barad-dûr to collapse, and ends his ability to return to physical form.
A common mix-up is 3021, the year the Third Age officially ends in Tolkien’s chronology when the Ring-bearers and the keepers of the Three Rings depart Middle-earth. The Ring itself is destroyed two years earlier, on 25 March 3019. Another nearby date is 3001, when Bilbo’s birthday party marks the beginning of Frodo’s possession of the Ring.