The outflow channels of Mars are widely believed to have formed through aqueous outbursts from aquifers, implying the past existence of large near-surface water reservoirs and the past operation of a vigorous hydrological cycle. However, accepted mechanisms of channel development suffer from numerous weaknesses, including (1) reliance upon implausible hydrological assumptions; (2) requirement of water abundances that are orders of magnitude greater than can be justified by geochemical considerations; (3) reliance upon long-term conditions that may be incongruous with the preserved mineralogical record; (4) limited correspondence between expected and observed channel properties; and (5) reliance upon exotic aqueous processes for which there are no known solar system analogs. In contrast, channel characteristics are consistent with volcanic origins involving low viscosity lava flows and associated processes of thermal or mechanical erosion. The volcanic hypothesis is founded upon the existence of analog landforms on multiple bodies of the inner solar system and on corresponding analog processes that are variations on familiar terrestrial volcanic themes. Volcanic channel origins are compatible with available mineralogical and geochemical data and are consistent with the nature of preserved channel landforms. The volcanic hypothesis fits within a wider geological framework that economically accounts for the existence and nature of large outflow systems located on the Moon, Venus, and Mars. A volcanic origin reduces the probability that extensive aqueous environments existed during the Hesperian and Amazonian along the outflow channels and in associated terminal basins, and it narrows the possible range of Martian environments once hospitable to life.