If you had talked to scientists about anti-gravity a few years ago, they would have said it's pure science fiction. That may have changed about 10 years ago when Eugene Podkletnov, at Tampere University of Technology in Finland notice a gravity shielding effect when experimenting with superconductors.
The experiment Podkletnov conducted was to magnetically levitate a large (approx. 12" diameter) YBa2Cu3O7 superconductor disk while rotating it at several thousand RPM. Any object held above that rotating superconducting disk supposedly lost anywhere from .5% to 2% of its mass (weight).
Pure fiction? The jury is still out. But NASA and a number of Universities have been investigating this phonomena for the last few years. NASA started the Delta G Experiment, led by scientist David Noever, to verify Podkletnov claims at the Marshall Space Flight Center.