Antiprotons don't have negative mass, they have positive mass. If a proton and an antiproton collide they literally obliterate one another and their mass is replaced by two gamma photons. Cool.
There is a cool story about its experimental discovery here.
The antiproton (p, pronounced p-bar) is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy. It was discovered in 1955 by University of California, Berkeley physicists Emilio Segrè and Owen Chamberlain, for which they were awarded the 1959 Nobel Prize in Physics. An antiproton consists of two up antiquark and one down antiquark (uud). The properties of the antiproton that have been measured all match the corresponding properties of the proton. The question of how matter is different from antimatter remains an open problem, in order to explain how our universe survived the Big Bang and why so little remains of antimatter today in our solar system.

funny story from my previous life in nuclear physics. Jack Sandweiss, professor of physics at Yale, was an operator of the Bevatron when he was a grad student. He and a couple of his friends bootlegged an experiment to discover the antiproton before the "official" experiment. The divided the emulsion foils up between then, and discovered the antiproton in the last foil, but that data was analyzed after the official experiment. If they had analyzed their data from back to front, they would have gotten a Nobel Prize while grad students (in reality, they never would have been allowed to claim)
Posted by: Bruce Libby | March 04, 2010 at 01:45 PM