A mass distribution for a sample of 129 DA white dwarfs is presented, based on fitting hydrogen line profiles to the predictions of stellar atmosphere models. The atmospheric parameters determined from spectroscopy are shown to be of improved accuracy over those obtained with other techniques. The spectroscopic masses are in good agreement with those inferred from gravitational redshift measurements. The comparison includes objects of particular astrophysical interest such as the Pleiades white dwarf LB 1497 (0.98 M .), and 40 Eri B (0.51 M .). The masses obtained for the stars in the Hyades cluster are found to be measurably higher than those of field stars. The surface gravities obtained from spectroscopy are also consistent with those obtained from trigonometric parallaxes although the observed scatter is greatly reduced in the spectroscopic analysis. The observed mass distribution exhibits a narrow peak, but broad and flat tails extend to large and small masses. The mean mass of the distribution is somewhat lower-near 0.56 M . -than found in the best previous analyses. The mode of the distribution is in the narrow mass range 0.50-0.55 M . , which contains more than 30% of the stars observed, and the median has a value of M = 0.54 M . . Nearly 10% of the stars have masses low enough that their existence must be ascribed to close binary evolution. Zuckerman & Becklin have found recently that two of those objects have low-mass nondegenerate companions. The high-mass tail includes one object (GD 50) near 1.3 M . . The consequences of these results for earlier phases of stellar evolution are discussed.