Shoe

 were a common item of clothing, worn by Humanoid species as fashion and to cover or protect the 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.

While the 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)

When the 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)