Anti-gravity

Anti-gravity, also known as anti-grav, was the process of creating objects free from or releasing objects from the force of gravity.

Time Lord technology
The Time Lords' Matrix held many advanced scientific techniques, including the secret of anti-gravity power. (TV: The Mysterious Planet)

The ancient Britons built Stonehenge with the aid of the Monk's anti-gravitational lift, according to the Monk himself. (TV: "Checkmate")

During the Siege of Trenzalore, the Eleventh Doctor overzealously repaired a toy car to the point of installing anti-gravs on it. (TV: The Time of the Doctor)

TARDIS
TARDIS corridors normally used anti-gravity, as the corridors went vertically as well as horizontally. House disabled the anti-gravity in the corridors of the Doctor's TARDIS in an attempt to kill Amy Pond and Rory Williams. (TV: The Doctor's Wife) Air corridors projected by TARDISes had the option to use anti-gravity, allowing the occupant of the corridor to float through the corridor instead of walk. (TV: The Time of Angels)

When the Eleventh Doctor attempted to get into Trenzalore, his TARDIS wouldn't let him and shut itself down nearby, everything apart from the anti-grav. The Doctor pulled out his sonic screwdriver and shut it down, which resulted in the TARDIS falling into Trenzalore. (TV: The Name of the Doctor)

Other occurrences
While on Rhoos, the First Doctor, Hill, Shelly and Chertzog used anti-gravity suits (which the Doctor called "contra-gravity suits") to rise up into the air and get a good look at their surroundings, which turned out be the giant Cyclops Fo. (PROSE: The Playthings of Fo)

The Tractators could use their control of gravity to release objects from gravity. (TV: Frontios)

An Arcadian representative possessed an anti-gravity umbrella. (COMIC: Smart Bombs)

A phenomenon occurred in a Korven Space-Time Manipulator located in Gryffen Manor, involving a white hole and a black hole moving together. This was part of Thorne's plan for the Korven invasion of Earth, as Alistair Gryffen would be forced to use the temporal stabiliser on the STM, which would allow the Korven invasion force through. Had Gryffen not used the stabiliser, the holes would combine, creating a stupendous vortex of anti-gravity, with anything within its reach being sucked into oblivion, this would have resulted in the entire Earth being sucked into the vortex. (TV: The Eclipse of the Korven)

The Anti-Grav Olympics were a version of the original Earth Olympic Games active in the mid-21st century. In 2074, the Eleventh Doctor rode an anti-gravity motorbike in the Anti-Grav Olympics and finished last. (TV: The Bells of Saint John)

The Fourth Doctor had an anti-gravity device installed in his car Bessie, which he would use to fly over obstacles. (COMIC: Death Flower)

The Eighth Doctor once told Charley Pollard that anti-grav technology was invented by Wilfred Jeffries "several hundred years" after Charley left Earth in 1930. (AUDIO: Sword of Orion)

A Rutan mothership around Earth was provided with an anti-grav system. The Fourth Doctor aimed to knock it out to prevent their invasion. (TV: Horror of Fang Rock)

The First Doctor speculated that the barges that the Voord used on Kandalinga were powered by anti-gravity. (PROSE: The Fishmen of Kandalinga)