Trainer
The Tenth Doctor wore Converse trainers, (TV: Time Crash [+]) coloured in cream, (TV: The Christmas Invasion [+]) black, (TV: Rise of the Cybermen [+]) red, (TV: Smith and Jones [+]) and yellow. (TV: The Infinite Quest [+]) Despite his protests, both his war and eleventh incarnations stated the trainers he wore were sandshoes. (TV: The Day of the Doctor [+])
The Fourteenth Doctor wore papyrus orange trainers, (TV: The Power of the Doctor) which were passed to the Fifteenth Doctor through bi-generation. (TV: The Giggle)
Rose Tyler wore trainers. (TV: Rose-Doomsday)
Clara Oswald wore Ash wedge trainers. (TV: Flatline, Face the Raven, Hell Bent)
Gwen Cooper wore moss and white trainers when she met met the cannibalistic Brynblaidd villagers. (TV: Countrycide [+])
Sam Jones was wearing trainers when she and the Eighth Doctor arrived in a swamp on Paratractis in an alternate 2108. (PROSE: Genocide) When she was in 1969, she briefly worried about her very 1990s-era trainers. (PROSE: Revolution Man)
In 2004, H.J. Hardeman saw the Ninth Doctor in an Oxfam in Sheffield, where he tried to exchange his "Edwardian gear" for jeans and trainers. (PROSE: Have You Seen This Man?)
Ryan Sinclair claimed that he and his colleagues used to put funny notes inside trainers at his workplace. (TV: Kerblam!)