Neutron data observed using the Neutron Spectrometer aboard 2001 Mars Odyssey provide a lower limit to the global inventory of Martian water-equivalent hydrogen. Hydrogen-rich deposits ranging between about 20% and 100% water-equivalent by mass are found poleward of ±50° latitude, and less rich, but significant, deposits are found at near-equatorial latitudes. The equatorial deposits between ±45° latitude range between 2% and 10% water-equivalent hydrogen by mass and reach their maximum in two regions that straddle the 0-km elevation contour. Higher water abundances, up to ∼11%, are required in subsurface regolith of some equatorial regions if the upper 10 g/cm2 of regolith is desiccated, as suggested on average by comparison of epithermal and fast neutron data. The hydrogen contents of surface soils in the latitude range between 50° and 80° north and south are equal within data uncertainties. A lower-limit estimate of the global inventory of near surface hydrogen amounts to a global water layer about 14 cm thick if the reservoir sampled from orbit is assumed to be 1 m thick.