Science fiction writers imagined anti-gravity as early as the 19th century including Percy Greg's Across the Zodiac (1880), C.C. Dail's Wilmoth the Wanderer (1890), John Jacob Astor's A Journey in Other Worlds (1894), and H.G. Wells' The First Men in the Moon (1901).
In his 1955 story "What Goes Up," Arthur C. Clarke describes his own version of a Cavorite-type anti-gravity field generated accidentally by a nuclear power plant. John W. Campbell's "Who Goes There?" (1938) deals with an alien who builds an anti-gravity personal jet pack.
In his 1970 novel Cities in Flight, James Blish envisions our descendants leaving Earth to travel through space, not in rocket ships or space stations, but in the actual cities of Earth -- New York, Los Angeles, Boston, San Francisco. The cities are launched into space using spin dizzies -- giant anti-gravity devices that generate a force field around a city and turn it into a self-contained, self-propelled space ship. In his 1971 short story "Something Wild is Loose," Robert Silverberg describes a rocket ship propelled by an antigravity device called a "gravity drinkers" which "spun on their axes, gobbling inertia and pushing up the acceleration."
What about anti-graving in real science? String theory, which posits that all matter and forces consists of vibrating, one-dimensional loops of energy, or "strings," also proposes 10 dimensions instead of the familiar four we know (three of space and one of time). According to a recent article in Scientific American (February, 2004), ordinary matter cannot escape into these extra dimensions. But gravity can. This leakage might warp the space time continuum, and if gravity is leaking out of our dimension, it would reduce the gravitational force in our universe. As a result, cosmic expansion might accelerate, and planetary motions could also be affected.