Has the gravitational interaction of antimatter ever been examined experimentally? I know that the gravitational interaction of antimatter is expected to be the same as normal matter.
But my question is, has it ever been experimentally validated?
I think it would not be a trivial experiment, because electromagnetic effects have to be eliminated, so neutral particles would be needed. Maybe diamagnetically trapped antihidrogen atoms could be examined as to which direction they fall?
 A: As well as the antihydrogen experiments, ALPHA, AEGIS and GBAR that were mentioned in other answers, there are a couple of other experiments, though they haven't had any results.
In the 60's, they tried the obvious thing of dropping positrons down a metal tube (paper), but it didn't work, for the subtle reason that the electrons in the metal sag under gravity also, producing just the right size of electric field to cancel out the gravitational acceleration.
There is also a proposal (example paper) and some groups working on (grant), making a free fall measurement on positronium (the bound state of an electron and positron). This measurement is tricky, because the two particles annihilate each other in short order.
A: The following has ben found via Wikipedia page “Gravitational interaction of antimatter”.
Another experimental test has been provided by the supernova SN1987a (anti)neutrinos, and this has been published in two brief reports in Phys. Rev. D in 1988 [1] and 1989 [2]. 
After the explosion of this supernova,  19 antineutrinos have been detected at IMB and Kamiokande on earth within a time wintow of 13s. Statistically, 3 to 4 of the events should be due to neutrinos instead of antineutrinos. If at least one of the 19 event involves a neutrino, which according to [2], had a probability higher than 90% (between 92% and 99%), then the fact that all events happened simultaneously tells us that they felt the same gravitational field from the Galaxy during their travel. More quantitatively, this field is estimated to have changed the travel time of the neutrino (and the light) by a few months (1 to 6 according to [1]), allowing to upper bound the “gravitational difference” between neutrinos and anti neutrinos to a few part per million. 
I have no idea whether this data has been analyzed since 1989, e.g. taking into account the 5 (anti)neutrino detected in the soviet Baksan Neutrino Observatory. But until another supernova explodes in the (not to close) neighbourhood, we probably won’t get much more experimental information on the relative weight of neutrinos and antineutrinos !
Bibliography


*

*J. M. LoSecco, “Limits on CP invariance in general relativity”, 
Phys. Rev. D 38, 3313 (1988). This paper is very short (half a page !), and easy to understand.

*Sandip Pakvasa, Walter A. Simmons, and Thomas J. Weiler,
“Test of equivalence principle for neutrinos and antineutrinos”,
Phys. Rev. D 39, 1761 (1989)
A: The only experiment I know of was done by the ALPHA team at CERN. The results are published in this paper. The error bounds are huge - all the team were able to say is that the upper limit for the gravitational mass of antihydrogen is no greater than 75 times its inertial mass! However I believe an updated version of the experiment, ALPHA2, is in progress and will hopefully be able to do a bit better.
Other planned experiments are AEGIS and GBAR, both also at CERN. However neither have made any measurements yet.
This may seem like slow progress, but antihydrogen is extraordinarily difficult stuff to handle as contact with any normal matter will annihilate the antihydrogen.
