Flying

Flying (TV: The Return of Doctor Mysterio) or levitation (COMIC: Levitation, TV: The Return of Doctor Mysterio) 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 flew. (TV: Let's Kill Hitler)

Animals

Birds had the ability to fly, including those on Hyspero. (PROSE: The Scarlet Empress)

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) In 2016, the energies of an artificial wormhole operated by the Celestial Hyperloop Corporation mutated several humans in San Francisco into gargoyles, the first stage of which was the ability to fly. (COMIC: The Transformed)

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) After his resurrection by the Disciples of Saxon, the Saxon Master himself was also observed to leap impossibly tall, although due to his incomplete resurrection, doing so siphoned away large swathes of his life force. (TV: The End of Time)

The Doctor learned to fly in their third 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) In their seventh incarnation, the Doctor used this ability once again. Roz Forrester once found the Doctor levitating while juggling balls of plasma and singing in three separate voices. (PROSE: Sky Pirates!) As he regained his memory of learning Venusian aikido, the Eighth Doctor recalled "flying through the air" before whirling back to face his Venusian instructor. (PROSE: The Eight Doctors)

However, later incarnations of the Doctor were not so keen to fly; the Fourth Doctor and Romana II briefly considered flying to get down from the Eiffel Tower, though they eventually took the lifts 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) As he made his way to the Zero Cabinet, the newly-regenerated Fifth Doctor promised Tegan Jovanka and Nyssa of Traken that they wouldn't have to feel his weight, as he would be levitating. (TV: Castrovalva)