Using detailed Monte Carlo calculations, the properties of runaway breakdown in the atmospheres of the four gas giant planets in our solar system are investigated, and the runaway avalanche lengths and average runaway electron kinetic energies are presented as a function of atmospheric electric field strengths. The runaway breakdown threshold field for the Jovian atmospheres is found to be 10 times smaller than the conventional breakdown field when hydrometeors are present, compared to 3 times smaller for Earth's atmosphere, indicating that runaway breakdown processes may be much more efficient in the gas giants than on Earth. In the Earth's atmosphere, runaway breakdown is known to produce large bursts of x-rays and gamma-rays from thunderstorms, such as terrestrial gamma-ray flashes, and may play a role in lightning initiation. These results suggest that runaway breakdown may play an important role in thunderstorm and lightning processes on the Jovian planets as well.