Shoes were a common item of clothing worn by humanoid species as fashion and to cover or protect their feet. Their presence was so typical in most cultures encountered that it was rare that they would be noticed specifically.
The Doctor and most of their companions wore shoes on most occasions, as it made the Doctor's main bit of advice — "Run!" — a bit easier on their feet[additional sources needed].
Susan Foreman lost one of her shoes on Marinus when it fell into a pool of acid and dissolved. (TV: The Keys of Marinus) Susan later had only one shoe when the First Doctor left her behind on 22nd century Earth. (TV: The Dalek Invasion of Earth) Jeremy Fitzoliver briefly lost one of his shoes when it got stuck in mud. (AUDIO: The Paradise of Death) Both of Harry Sullivan's shoes were destroyed by the auto guard on the Nerva. His second shoe was deliberately thrown across the room by the Fourth Doctor, in an attempt to distract the guard, which targeted organic matter. (TV: The Ark in Space)
Leela had strong feelings about footwear, thinking high heels impractical, and preferred to engage in combat barefoot, (AUDIO: The Renaissance Man) though she did typically wear leather boots. (TV: Image of the Fendahl, Underworld, The Invasion of Time)
Indeed, Romana I came to regret wearing high heels, which the Fourth Doctor warned her would not be suitable. By the time she admitted they were not practical, Romana's feet were sore, and she could not go on. She later discarded her shoes entirely, and simply travelled barefoot. In the TARDIS, the Doctor found Romana a pair of more sensible boots, for which Romana was thankful. (TV: The Stones of Blood) Polly Wright also found that her shoes were a hindrance to running fast with soldiers behind her in pursuit, and removed them in order to keep up with Kirsty McLaren. (TV: The Highlanders)
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) After his own regeneration, the Fourth Doctor searched his person for his TARDIS key before remembering it was in his shoe. (TV: Robot)
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 as well. (TV: Smith and Jones)
The Tenth Doctor wore trainers on his travels, the colour of which 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 weren't, the War Doctor responded by saying, "Yes, they are." (TV: The Day of the Doctor)
The Tenth Doctor complimented Martha Jones on the shoes she wore to the party commemorating the unveiling of Richard Lazarus hypersonic soundwave manipulator. (TV: The Lazarus Experiment)
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)
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)
The Thirteenth Doctor wore laced-up boots that were good for running, (TV: The Woman Who Fell to Earth, COMIC: A New Beginning, et al.) but sometimes wished for Wellington boots instead. (TV: The Battle of Ranskoor Av Kolos)
In the year 200,100 on The Weakest Link, Rose Tyler was asked in what area of fashion Stella Bopbates was famous in. She incorrectly guessed shoes; the correct answer was hats. (TV: Bad Wolf)