Harry Houdini

Harry Houdini was a famous magician on Earth. He met the Doctor and taught him how to contract the muscles, which helped the Doctor escape from the Eight Legs on Metebelis III. (DW: Planet of the Spiders)

Between 1917 and 1920, Houdini, along with Sir Arthur Conan Doyle, publicly announced the existence of fairies following the release of the Cottingley fairy photos. Gwen Cooper believed this was all an act of self-publicity. (TW: Small Worlds)

On Avalon, the First Doctor used a trick he learned from Houdini to make an egg appear from Gramling's beard. (MA: The Sorcerer's Apprentice)

While tied up on Nerva Beacon, the Fourth Doctor recalled an encounter with Houdini. (DW: Revenge of the Cybermen)

The Seventh Doctor attempted to use Houdini's trick of contracting the muscles to escape from the Process's cocoon, but it was too tight. (NA: Cat's Cradle: Time's Crucible)

On Mendeb Three, the Seventh Doctor told Bep-Wor that he had been taught by Houdini, but hadn't needed to use any of the tricks he had learned to escape from his chains. (PDA: Independence Day)

The Eighth Doctor mentioned that he had taken lessons in escapology from Houdini. (EDA: Frontier Worlds)

The Eighth Doctor met Houdini when he was travelling with Lucie Miller. Houdini taught Lucie how to escape from handcuffs during this time. (ST: The Great Escapes)

Whilst handcuffed, Donna questioned the Tenth Doctor as to whether he had ever met Houdini. (DW: Planet of the Ood)

In Area 51, when the Doctor, Cassie, and Jimmy were trapped on a 'table', the Doctor used a trick taught to him by Houdini to break out of the handcuffs and turn off the amnesia gas. (DW: Dreamland)

The Eleventh Doctor, in 16th century Venice, entered an underground cellar and met five female "vampires". When he saw that they could not be seen in the mirror, he compared it to a trick by Houdini. (DW: The Vampires of Venice)

On Poseidon 8, the Doctor escaped from being bound by ropes to a railing, saying he learned the trick from a "long story" with Houdini. (VG: Shadows of the Vashta Nerada)

Behind the scenes
Houdini actually never investigated the Cottingly photos, despite some correspondence from Conan Doyle that suggested he visit. Houdini was shown to be involved in the events in the 1997 film FairyTale: A True Story.