While it's never been tested experimentally due to how difficult it is to create and store the stuff, it's disappointingly likely that antimatter will fall "down" just like regular matter. The thinking behind this is that antimatter (despite the "anti-") is made of regular ordinary energy, and even if it's got an opposite charge, it should still obey the same general rules as matter does. Antimatter falling up would mean a violation of the law of conservation of energy, among other things.
That said, if antimatter were to exhibit antigravity, it would go a long way towards explaining some of the peculiarities of our universe. For example, the universe is supposed to have just as much antimatter as it does matter, but we don't know where the antimatter is. If antimatter and normal matter repelled each other, it could mean that there are entire antimatter galaxies out there. Also, that repulsion would explain why the universe is not just expanding, but speeding up its expansion, something that's tricky to figure out when everything in the universe is always attracted towards everything else.
In either case, the team at CERN should be able to put the debate to rest within a couple months, when they plan to trap a blob of antihydrogen and then just watch it to see which way it falls. Down, and the laws of physics stay in place. Up, and you might just get that hoverboard you've always wanted.
Via Technology Review