Agamemnon was ordered in 1777 from the shipbuilder Henry Adams at Bucklers Hard, a small yard on the Beaulieu River, and built from oak felled in the surrounding New Forest. She cost just over £38,000 and was launched in April 1781. The future Lord Nelson took command in January 1793 and held it for more than three years, and the bond formed then never broke. Even as the ship aged into a leaky, repair-hungry burden that the navy nearly scrapped in 1802, Nelson's regard for her endured. She was, in the language of his biographers, simply his favorite, the deck where a rising officer had felt most himself.

Few ships were worked harder. Agamemnon helped capture French convoys in the Bay of Biscay, fought at the Battle of the Saintes in 1782, and carried Nelson's seamen ashore to take the Corsican town of Bastia after a 40-day siege. She chased the French at the Battle of Genoa and ran aground at the first Battle of Copenhagen in 1801, flying signals of distress as the battle roared past her stranded hull. Twice she nearly foundered on rocks off Cornwall, limping into port lashed to other vessels to keep from sinking. Her timbers were never sound for long. The navy patched her, refitted her, and sent her back out, because a fighting ship, even a tired one, was too valuable to waste.

On 21 October 1805, Agamemnon took her place eighth in Nelson's weather column at the Battle of Trafalgar. In the smoke and thunder she came up against the Santísima Trinidad, the largest warship afloat, a Spanish four-decker that dwarfed her. Agamemnon poured fire into the giant until it was dismasted and broken. By the time the Spanish ship struck her colors, 216 of her crew were dead, a toll that measures the savagery of close-range gunnery between wooden walls. Agamemnon herself came through with just two men killed and eight wounded. Below decks on a nearby ship, Nelson lay dying. His favorite vessel had outfought one of the mightiest ships in the world, and survived to mourn him.

Agamemnon's last years carried her to South American waters off Brazil and the Río de la Plata. By 1809 she was worn out, her defects catalogued in detail by her own carpenter. In June, working between Gorriti Island and the shore near Maldonado, she struck an uncharted shoal. Captain Jonas Rose tried everything, hauling on anchors to drag her free, but her dropped anchor had pierced her own hull, and she would not move. On 17 June, listing hard to starboard, she was abandoned. Crucially, no one died. Every member of the crew and most of the ship's stores were taken off safely by boats from the squadron, and a court-martial honorably cleared Rose, blaming the ship's decrepit condition rather than the man. In 1993 a sonar operator named Crayton Fenn located her wreck north of Gorriti Island, and divers later recovered her artifacts, including one of her cannons and a seal bearing the name Nelson.