Spirit's Mössbauer (MB) instrument determined the Fe mineralogy and oxidation state of 71 rocks and 43 soils during its exploration of the Gusev plains and the Columbia Hills (West Spur, Husband Hill, Haskin Ridge, northern Inner Basin, and Home Plate) on Mars. The plains are predominantly float rocks and soil derived from olivine basalts. Outcrops at West Spur and on Husband Hill have experienced pervasive aqueous alteration as indicated by the presence of goethite. Olivine-rich outcrops in a possible mafic/ultramafic horizon are present on Haskin Ridge. Relatively unaltered basalt and olivine basalt float rocks occur at isolated locations throughout the Columbia Hills. Basalt and olivine basalt outcrops are found at and near Home Plate, a putative hydrovolcanic structure. At least three pyroxene compositions are indicated by MB data. MB spectra of outcrops Barnhill and Torquas resemble palagonitic material and thus possible supergene aqueous alteration. Deposits of Fe3+-sulfate soil, located at Paso Robles, Arad, and Tyrone, are likely products of acid sulfate fumarolic and/or hydrothermal activity, possibly in connection with Home Plate volcanism. Hematite-rich outcrops between Home Plate and Tyrone (e.g., Montalva) may also be products of this aqueous activity. Low water-to-rock ratios (isochemical alteration) are implied during palagonite, goethite, and hematite formation because bulk chemical compositions are basaltic (SO3-free basis). High water-to-rock ratios (leaching) under acid sulfate conditions are implied for the high-SiO2 rock and soil in Eastern Valley and the float rock FuzzySmith, which has possible pyrite/marcasite as a hydrothermal alteration product.