In Star Trek, anti-grav units were device capable of nullifying the force of gravity and were used to lift loads of an extremely high mass. These were available as hand-held devices, in the form of pallets or as larger anti-grav sleds.  Another form of the device - the anti-grav lift - was to carry away wounded crew members. The exact form of this gravity-manipulating technology is never explained but it presumably worked along the same gravitational shielding principles as the artificial gravity systems in Starships, only in reverse.

In real science, such feats of levitation have been accomplished using giant superconducting magnets that create a magnetic field that distorts the orbits of the electrons in the atoms of any object placed in its path. In 1997, a team led by Andrey Geim managed to levitate several small objects, including live frogs, mice, and grasshoppers, in a large magnetic field at the High Field Magnet Laboratory in the Netherlands.

Anti-grav sled
Such technology, however, does not actually manipulate gravity - it only overcomes it. In 1992, a Russian scientist Yevgeny Podkletnov reported producing a true anti-gravity or gravitational shielding effect using a device consisting of a spinning, super-conducting ceramic ring, solenoids that generated a magnetic field and liquid nitrogen acting as a coolant. Recent work done by Martin Tajmar supported by the European Space Agency demonstrated that an acceleration field can be induced by applying angular accelerations to a superconductor. This superconductive gyroscope was capable of generating a powerful gravitomagnetic field - the gravitational counterpart of the magnetic coil. By allowing force-carrying gravitational particles, known as the gravitons, to become heavier, they found that the unexpectedly large gravitomagnetic force could be modelled. Further developments on superconductors and gravitomagnetic technology could well yield devices that could leviate objects, generate tractor beams and be the basis for a general-purpose force field.

The Podkletnov Experiment