Flying

Flying (TV: The Return of Doctor Mysterio) or levitation (COMIC: Levitation) was the ability of a living being to carry itself in the air without touching the ground.

Similar movement from a mechanical device was known as flight, (TV: The Parting of the Ways) although the verb "flying" could also be used to refer to the action of driving a vehicle such as a TARDIS, whether or not it actually flied. (TV: Let's Kill Hitler)

Animals

The Tenth Doctor and Rose Tyler once encountered flying stingrays, (TV: Army of Ghosts) and flying creatures were found by Bernice Summerfield on the planet Javarda. (WC: Dead and Buried)

Sapient beings

In humans, it was considered a superpower. Among the Ghost's superpowers was "basic" flying, which he used to get about the city in the course of his crime-fighting. (TV: The Return of Doctor Mysterio)

Time Lords occasionally displayed, or referred to, an ability to fly. Due to his coordinates having "slipped", the Time Lord messenger who warned the Third Doctor of the Master's presence on Earth materialized hovering in the air, an error he soon corrected. (TV: Terror of the Autons) The Doctor learned to fly in their second incarnation from the book Levitation Universal Edition, and gleefully used this newfound ability in the course of his regular activities for some time after discovering the "talent" he had for it. (COMIC: Levitation) However, later incarnations of the Doctor were not so keen to fly; the Fourth Doctor and Romana II briefly considered flying to get to the top of the Tower, though they eventually took the lifts up the Eiffel Tower because flying would have been too conspicuous. (TV: City of Death) As part of a scheme to be carried out by both himself and the Fourth Doctor, Drax told the Doctor he could "fly over there and shut the door", although this plan was not carried out. (TV: The Armageddon Factor)