When and where has the last battle between sail-powered ships been fought? If possible, please include the countries involved as well as the armament and types of ships.
Battle of Sinop between Ottoman and Russian empires during Crimean war seems to be the last major naval battle with sail-powered ships. There were three steamboats in Russian fleet, and one steam boat in Ottoman fleet, but their firepower was negligible compared to sail-powered ships involed in the battle.
It was in 1853, Russian fleet destroyed Ottoman fleet in a bay of Sinop, and it was one of factors that brought England and France into the war with Russia.
http://ru.wikipedia.org/wiki/Синопское_сражение (more detailed description of battle course in Russian)
That would the Battle of Navarino fought during the Greek War for Independence in 1827. It was the last battle feature entirely sail fleets. Navarino is known as Pylos now. Sailing ships have come back into vogue recently so who knows how long they will be around and what was they might be involved in. The last active sailing warship appears to have been the Valmy. Modern Pirates are known to sometimes use sailing vessels.
It wasn't much of a battle, but according to Morison's history of the US Navy in WWII, the last engagement was between a couple of Chinese junks, and was settled by boarding. The bazooka did make it seem less like a 19th Century battle.
I agree that the battle of Sinop was the last significant battle with sailing ships on both sides. However, if we are talking of a military use of sailing ships, the last one was probably the German commerce raider Seeadler. It sank or captured 16 Entente ships in WW I.
See Wikipedia, and references there.