Anti-gravity

Anti-gravity 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 Monk, a renegade Time Lord, used anti-gravity lifts to complete Stonehenge on Earth circa 1500 BC. (TV: The Time Meddler)

TARDIS
TARDIS corridors normally used anti-gravity, as the corridors went vertically as well as horizontally. House disabled the anti-gravity in the corridors 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, the 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 occurences
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 occured 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 a anti-gravity motorbike in the Anti-Grav Olympics and finished last. (TV: The Bells of Saint John)

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)
 * The Eight Doctor might refer to Earth only.

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)