RMS Titanic

The RMS Titanic was a luxury ocean liner on Earth in the early 20th century, noted as being the largest steamship of its time, carrying 2,223 passengers. (TV: Let's Kill Hitler) It was famously called "unsinkable", yet sank on its maiden voyage on 15 April 1912 after colliding with an iceberg. (TV: The Invasion of Time)

The Seventh Doctor, Ace and Bernice Summerfield travelled to the Titanic, tracking Huitzilin. They were on the ship when it collided with the iceberg. The Doctor noted that the event of its sinking was part of the Web of Time. (PROSE: The Left-Handed Hummingbird)

El Ape, a temporary travelling companion of the Seventh Doctor, actually caused the ship to sink. (COMIC: Follow That TARDIS!)

The Master, trapped on Earth in the early 20th century, boarded the Titanic when it sank, to avoid the upcoming First World War by migrating to the United States of America. (AUDIO: Mastermind)

The Fourth Doctor had an issue of the Daily Mirror describing the disaster, which he saw Borusa reading. On noticing this, the Doctor promised that he had nothing to do with the ship's destruction. (TV: The Invasion of Time)

The Ninth Doctor persuaded several people to not board the liner on its maiden voyage. (TV: Rose) He later told Jabe that he had once been on a ship that "they said was unsinkable." He "ended up clinging to [the] iceberg," commentating that "it wasn't half cold." (TV: The End of the World)

The Eleventh Doctor was on the Titanic shortly before he visited Klimtenburg. The voyage soaked one of his napkins. (PROSE: Plague of the Cybermen)

Following the sinking, measures were taken place to see that such an accident would not occur again. To that end, the International Ice Patrol was formed and future ships would have round-the-clock radio surveillance and lifeboats for everyone. As the Seventh Doctor noted to Cristián Alvarez, to prevent the Titanic disaster would condemn future passengers. (PROSE: The Left-Handed Hummingbird)

When asked by her teacher why the Titanic sank, Mels said it was because the Doctor didn't save it, and then called the teacher stupid for not knowing. This got her sent to the head teacher's office. (TV: Let's Kill Hitler)

Recreation
Max Capricorn, the head of Max Capricorn Cruiseliners, constructed a starship replica of the Titanic for a voyage from Sto to Earth for the observation of "primitive cultures" on Christmas Day 2008. According to one of the Heavenly Host, the name of the replica was chosen as "the most famous vessel of the planet Earth". (TV: Voyage of the Damned)