The surface of Mars preserves landforms associated with the largest known water floods. While most of these megafloods occurred more than 1 Ga ago, recent spacecraft images document a phase of outburst flooding and associated volcanism that seems no older than tens of millions of years. The megafloods that formed the Martian outflow channels had maximum discharges comparable to those of Earth’s ocean currents and its thermohaline circulation. On both Earth and Mars, abrupt and episodic operations of these megascale processes have been major factors in global climatic change. On relatively short time scales, by their influence on oceanic circulation, Earth’s Pleistocene megafloods probably (1) induced the Younger Dryas cooling of 12.8 ka ago, and (2) initiated the Bond cycles of ocean-climate oscillation with their associated Heinrich events of “iceberg armadas” into the North Atlantic. The Martian megafloods are hypothesized to have induced the episodic formation of a northern plains “ocean,” which, with contemporaneous volcanism, led to relatively brief periods of enhanced hydrological cycling on the land surface (the “MEGAOUTFLO Hypothesis”). This process of episodic short-duration climate change on Mars, operating at intervals of hundreds of millions of years, has parallels in the Neoproterozoic glaciation of Earth (the “Snowball Earth Hypothesis”). Both phenomena are theorized to involve abrupt and spectacular planet-wide climate oscillations, and associated feedbacks with ocean circulation, land-surface weathering, glaciation, and atmospheric carbon dioxide. The critical factors for megascale environmental change on both Mars and Earth seem to be associated tectonics and volcanism, plus the abundance of water for planetary cycling. Some of the most important events in planetary history, including those of the biosphere, seem to be tied to cataclysmic episodes of massive hydrological change.