I hope this is the right place to ask this question. It seems as though we never hear about ships from that time period still being sailed or at least stored and cared for.
There are several ships from this era still around. One of the oldest is HMS Victory, Horatio Nelson's flagship at Trafalgar. Laid down in 1759, she is a 100-106 gun First Rate. Following 13 years laid up in ordinary, during the peace between the end of the 7 Years War and the start of the American Revolutionary War, she would be commissioned into the Royal Navy in 1778. Following this, she took part in several major naval battles, including the First and Second Battles of Ushant and the Battle of Cape St Vincent. However, her most famous battle was Trafalgar, where Nelson's command would destroy the combined Franco-Spanish fleet in 1805. During the battle, Nelson would be shot in the back, and died aboard her. Following the battle, she served with distinction in the Baltic as the flagship of Sir James Saumarez. From 1812, she was moored as a depot ship in Portsmouth Harbour, where she would remain. In 1889, she would be turned into a school for naval signallers. Over time, she mouldered at her moorings - she was rammed by HMS Neptune in 1903, causing major damage to her. Without royal intervention, she might have been scrapped. In 1921, Sir James Caird helped found a campaign to save her, and in 1922, she was moved into a drydock in Portsmouth Naval Dockyard. By 1929, the vital repairs were completed, though some were still ongoing by WW2. In 1941, she was damaged by a Luftwaffe bomb, which blew away some of the cradles supporting her, and damaged her hull. She's still there today, and can be visited. Other surviving RN warships from this time include HMS Unicorn, a frigate launched in 1824 and now in Dundee and HMS Trincomalee (launched 1817), a frigate of the same class, now in Hartlepool.
Many, young Americans I might think, that the Battle of Hampton Roads and their use of Ironclad-ships were the first series of ironclad ships used by any country. T'is not the case. You have USS Constitution, oldest activated warship in the world, you have HMS Victory, a beautiful British-made ship described better below me, or above depending on position, and you have the unmentioned ship my other fellow historians hadn't mentioned.
HMS Warrior.
The French, ironically, were the first to invent an ironclad warship, not the British or the Americans, but eventually the British followed with HMS Warrior, a beautiful iron ship used, I believe, in the Opium Wars with China.
Cheers!