High-resolution Fourier spectra in the 0.9-2.5 μm region were measured for sixteen asteroids. These data were combined with 0.3-1.1 μm spectrophotometry and 3.0-3.5 μm narrowband photometry for compositional analysis. Comparison spectra of meteorites and terrestrial minerals were measured in the laboratory, some under simulated asteroidal conditions of pressure and temperature. Spectra of eleven representative S-type asteroids show a range of olivine/pyroxene ratios overlapping those of ordinary and carbonaceous chondrites, but not approaching those of common differentiated meteorite types. The reddening in the asteroid spectra implies the presence of metallic iron, but if the metal is finely divided its abundance could be low. S-type asteroids have spectra most consistent with undifferentiated compositions, and some of them, especially 8 Flora, could be ordinary chondrite parent bodies. 4 Vesta and 349 Dembowska are unusual asteroids which have spectra resembling those of achondritic meteorites. Vesta has a pyroxene-feldspar mineralogy intermediate in composition between eucrites and howardites. If shergottite-like basalts are present, they must be in low abundance. Dembowska has an olivine-pyroxene mineralogy similar in some ways to ordinary chondrites, but there is considerable evidence that it is actually a fragment of the mantle of a differentiated Vesta-like parent body. The most diagnostic spectral feature seen on three low-albedo asteroids is the 3 μm band due to water of hydration. 1 Ceres must consist mostly of a low-iron clay mineral with some hydrated salts. 2 Pallas has a low abundance of hydrated minerals relative to Ceres, with the bulk of its composition being anhydrous iron-free silicates. 324 Bamberga probably contains clay minerals, but its spectrum is dominated by abundant magnetite. These and other C-type asteroids have surface compositions consistent with massive aqueous alteration of primary carbonaceous chondrite minerals. These results all indicate that the compositions of main belt asteroids are more closely related to the compositions of meteorites than was previously believed. S-type and C-type asteroids are undifferentiated assemblages of which ordinary and carbonaceous chondrites are an incomplete sample. Differentiated meteorites could be derived from the other relatively rare asteroid types.