Antimatter has opposite electrical charge (and magnetic moment) from normal matter. It should have the exact same mass and interaction with gravity as normal matter.

An anti-electron is called a positron because it has a positive charge instead of negative. Antiproton (sometimes called negatron, but rarely) is just a proton with opposite charge. You can even make a hydrogen atom out of an antiproton and a positron, called antihydrogen. https://secure.wikimedia.org/wikipedia/en/wiki/Antihydrogen

I meant falling downwards towards the surface of the earth which would experimentally show that there is an attractive force between matter and antimatter. Experimentally showing that antimatter gravitationally attracts antimatter is next to impossible for technical reasons but there is even less doubt about this than about matter attracting antimatter. No matter how sure we think we are about something we can also be wrong though. Experiment gives us the final word (albeit with statistical limitations) and there have been numerous times in history where established theories have been flipped upside down by experiments.