Numerical models of Martian hydrothermal systems demonstrate that systems associated with magmatic intrusions greater than several hundred cubic kilometers can provide sufficient groundwater outflow to form the observed fluvial valleys, if subsurface permeability exceeds about 1.0 darcy. Groundwater outflow increases with increasing intrusion volume and subsurface permeability and is relatively insensitive to intrusion depth and subsurface porosity within the range considered here. Hydrothermally-derived fluids can melt through 1 to 2 km thick ice-rich permafrost layers in several thousand years. Hydrothermal systems thus provide a viable alternative to rainfall for providing surface water for valley formation. This mechanism can form fluvial valleys not only during the postulated early warm, wet climatic epoch, but also during more recent epochs when atmospheric conditions did not favor atmospheric cycling of water. The clustered distribution of the valley networks on a given geologic surface or terrain unit of Mars may also be more compatible with localized, hydrothermally-driven groundwater outflow than regional rainfall. Hydrothermal centers on Mars may have provided appropriate environments for the initiation of life or final oases for the long-term persistence of life.