Mary Celeste

The Mary or Marie Celeste was a ship famous for the mystery surrounding why it had been abandoned at sea. The First Doctor, Ian, Barbara and Vicki materialised on the ship. Daleks had already arrived via their Dalek time machines. The crew of the Celeste mistook the Daleks for "the Barbary Terror", and jumped overboard. The Doctor and his companions were unaware of the name of the ship they had landed on. (DW: The Chase)

Alternative Timelines
Its abandonment apparently was not a fixed point in time, as there were several different accounts of the event. The first three incarnations of the Doctor were all involved in different sets of experiences surrounding the crew's disappearance, though only the Second Doctor knew he was on the ill-fated vessel.

Another account had it that the Daleks on the ship had actually arrived via a human-made Time-Conveyor and that they were being pursued by two human brothers named Peter and David. These time travellers also left without realising the name of the ship. (DWAN: Timechase)

Yet a third said that the Second Doctor, Jamie and Zoe found that the crew of the Marie Celeste had been abducted by Arcturans. The Doctor freed the crew, but they were all killed by a sea serpent. Their experience of the ship was different from those of other time travellers on board the vessel, in that they actually knew they were on the Celeste. (DWAN: The Mystery of the Marie Celeste) Logically, then, this was the only solution to the mystery of the Celeste that the Doctor remembered.

A fourth history put the Third Doctor into the mix. When he landed the TARDIS on the New York docks, the crew of the Celeste mistook it for cargo and had it loaded on board. To regain access to his ship, the Doctor paid for passage on the Marie Celeste. When he showed Professor Theodore Cassells the TARDIS interior, he fled from the hold to the deck. When he tried to tell the captain what he saw, the captain misunderstood and thought the TARDIS was a time bomb. He, Cassells and the crew left the Marie Celeste in a lifeboat, which was swamped by a large wave that drowned everyone on it. The Doctor left, unaware of the name of the ship he was on. (TVA: A Stitch in Time)

References made to the ship

 * Sarah Jane Smith asked Harry Sullivan if he also though the apparently abandoned galleon in space was an "interplanetary Mary Celeste". (DWAN: Avast There!)
 * Tegan Jovanka told Nyssa that Mawdryn's ship was more Mary Celeste than Queen Mary, due to its apparently empty state. (DW: Mawdryn Undead)
 * Fitz Kreiner and Sasha found a building that was completely empty. Fitz likened it to the Celeste. (EDA: History 101)
 * In 2009, a future version of Peri Brown claimed that the Mary Celeste disappearance was caused by Piscons wanting to take over human forms. This was later revealed as simply something she made up. (CC: Peri and the Piscon Paradox)
 * Amy Pond compared an apparently deserted science research centre to the Mary Celeste. The Doctor said he didn't want to go through that trouble again. (NSA: Heart of Stone)
 * Rory Williams once asked the Doctor if he had anything to do with the mystery of the missing crew of the Mary Celeste to which the Doctor replied, "Not directly. Long story". (NSA: The Good, the Bad and the Alien)

Behind the scenes

 * In reality, the disappearance of the crew of the Mary Celeste remains a mystery on par with the disappearance of Amelia Earhart.
 * On the DVD release of The Chase, it's mentioned that some feel the nameplate seen in the episode is misspelled, but the production notes commentary indicates the spelling used is correct. Though Mary is technically correct, Marie was popularised when Sir Arthur Conan Doyle wrote the first fictional account of the ship and misspelled the name. This account became ubiquitous when some 19th century newspapers mistook Conan Doyle's fiction for fact. Through the years, many fictional accounts have traced their way back to Conan Doyle's original account. The net result has been widespread confusion — as expressed in DCOM: The Chase — over whether Mary or Marie is the correct spelling.
 * Although mostly played for laughs, the scene in which the Daleks force the passengers to jump overboard takes on a sombre note as a baby is shown among those falling into sea, becoming the first baby to die during the course of a televised Doctor Who story.