Each of the large Tharsis Montes volcanoes in the equatorial region of Mars has an unusual Amazonian-aged fan-shaped deposit on its west-northwestern flank. On the basis of Viking Orbiter data, the origin of these deposits has been variously ascribed to volcanic, mass-wasting, tectonic, and glacial processes. Using new MGS and Odyssey data, combined with recent developments in the study of cold-based glaciers, we reassess the geology and mode of origin for these deposits with particular emphasis on Pavonis Mons. The deposits share three characteristic facies, including (1) a ridged facies, consisting of tens to >100 parallel, concentric ridges around the margins of the deposits, (2) a knobby facies composed of irregular hills and hummocks, and (3) a smooth facies of broad, lobate plains that superposes all other units within the deposits. On the basis of morphology, topography, superposition relationships, and close terrestrial analogs in the Dry Valleys of Antarctica, we interpret the Pavonis fan-shaped deposit as the depositional remains of a cold-based glacier that formed on the northwestern flank in recent Martian history. We interpret the ridged facies as drop moraines formed around the margins of a retreating cold-based glacier, the knobby facies as a sublimation till derived from in situ down-wasting of cold-based glacial ice, and the smooth facies as extant debris-covered glacial ice. In addition to the three main facies, the fan-shaped deposit at Pavonis Mons contains several unique features, including arcuate scarps, high-relief flow-like features, and radial ridges, which suggest that volcanism played a role during its formation. Using recent results from Mars general circulation model simulations, we outline a model of glacier formation involving atmospheric deposition of water ice on the northwestern flanks of the Tharsis Montes during periods of high mean obliquity. Reconstructed ice sheet profiles for each of the Tharsis Montes glaciers suggest that the ice sheets attained average thicknesses of ~1.6--2.4 km, values that are consistent with a cold-based glacial origin. Analysis of crater size-frequency distributions using new data indicates that the age of the glaciation lies within the Late Amazonian (~10--200 Ma). Thus our results suggest that multiple phases of tropical mountain glaciation occurred on Mars within the past few hundred Myr and that significant amounts of near-surface, equatorial ice may remain within the deposit today.