The Mary Celeste was a ship, a brigantine. It received the name after 12 years as the Amazon, when due to damage it was sold at a salvage auction. The new owners repaired it, renamed it, and made Benjamin Briggs the captain; on 7 November 1872 he, his wife and daughter, and eight crew members left New York, bound for Genoa, Italy.

A month later, it was found drifting in the Atlantic Ocean between the Azores and Portugal by a ship, the Dei Gratia, which had left New York a week later. The sails were set in place, but there was water in the hold, no people on board and the lifeboat was gone. The weather had been rough and the Dei Gratia had encountered several storms; the simplest explanation for the Mary Celeste's desertion is that the people on board thought the ship was in danger of sinking, fled in the lifeboat, and were themselves lost at sea.

However, in 1883 Sir Arthur Conan Doyle under a pseudonym wrote a story, "J. Habakuk Jephson's Statement," about a ship called the Marie Celeste, using some of the facts from the real-life Mary Celeste. His story had the boat being involved in some sort of race-related mutiny and taken over by the black seamen on board. (In real life, the crew were mostly Dutch.) It was well-known enough to be officially denied.

Since then, the story of the ship has taken its place among the interesting mysteries that people enjoy speculating on. Theories include a seaquake, the barrels of alcohol in the hold exploding, and alien kidnapping. It is often associated with the occult and the Bermuda Triangle stories (despite the fact that it went nowhere near the area). The actual ship was refurbished and continued in use for eleven more years, though it was regarded as unlucky. Eventually it was beached in Haiti and allowed to rot, not being worth salvaging.

Sources:
http://www.fortogden.com/maryceleste.html
http://blindkat.tripod.com/triangle/mc.html
http://www.pagebypagebooks.com/Arthur_Conan_Doyle/
The_Captain_of_the_Polestar/index.html
http://www.occultopedia.com/m/mary_celeste.htm
http://www.gibnynex.gi/home/jimwatt/mary/part2.htm
http://www.i5ive.com/article.cfm/titanic/30127