Shoe

Shoes were a common item of clothing worn by humanoid species as fashion and to cover or protect their feet. Their presence was so usual in most cultures encountered that it was rare that they would be noticed specifically.

The Doctor and most of his companions wore shoes on most occasions, as it made his main bit of advice — "Run!" — a bit easier on their feet.

Susan Foreman lost one of her shoes on Marinus when it fell into a pool of acid and dissolved. (TV: The Keys of Marinus)

When the newly regenerated Third Doctor was found unconscious by UNIT soldiers, he was taken to the hospital. The hospital nurse, who was already concerned about his unusual vital signs and diagnostic test results, found him leaning out of bed, muttering about shoes. She put him back to bed and he appeared to fall asleep. When he later got to his shoes, the TARDIS key was hidden in one. (TV: Spearhead from Space)

Grace Holloway gave the Eighth Doctor a pair of shoes which originally belonged to her ex-boyfriend Brian. After wearing them for a while, the Doctor claimed they "fit perfectly". (TV: Doctor Who)

While the Tenth Doctor was trapped on the Moon with Martha Jones in the Royal Hope Hospital, he used the sonic screwdriver to multiply the output of an X-ray machine to use it as a weapon to stop the Slab that was chasing him. When Martha questioned him about the dose of radiation, the Doctor told her roentgen radiation wasn't dangerous to him. He squirmed around, saying he was concentrating to expel it into one of his shoes, then threw the shoe in the trash. When Martha called him mad, he said, "You're right. I'd look daft with one shoe," and threw the other in the trash to go barefoot. (TV: Smith and Jones)

River Song walked on Alfava Metraxis with her red high heel shoes in her hand when she signalled Father Octavian at the crash of the Byzantium. (TV: The Time of Angels) An identical pair of shoes were present in the UNIT Black Archive. (TV: The Day of the Doctor)

The Tenth Doctor wore trainers on his travels, the colour of which he varied from adventure to adventure. When he met his War and Eleventh incarnations, the latter kept calling them sandshoes; when the Tenth Doctor insisted that they're weren't, the War Doctor responded by saying "Yes, they are." (TV: The Day of the Doctor)

When the Eleventh Doctor went to St John's Monastery in the 22nd century to meet the early version of the Flesh, he stepped in some of the acid that they were mining. He removed his shoes and then borrowed another pair from the miners. When the Eleventh Doctor Ganger arrived, then stabilised, they encouraged the others to use the shoes to tell them apart, then switched shoes so that the Doctor and his Ganger could assess Amy. (TV: The Rebel Flesh, The Almost People)