The atmospheric parameters, T-eff and log g, have been determined for a sample of 52 hydrogen-line (DA) white dwarfs by fitting optical spectra to theoretical model atmospheres. Multiple observations of each star allow an estimation of the accuracy of the method: the average external errors are 490 K in T-eff and 0.06 in log g. Masses have been derived using white dwarf evolutionary models where finite temperature effects are taken into account. The average mass of the 46 DA stars in our sample with T-eff > 12,000 K is 0.587 M., with a dispersion of 0.166 M. while the mode of the distribution is between 0.50 and 0.55 M.. The mass distribution shows a low-mass (M < 0.4 M.) tail of four objects which are most likely helium white dwarfs, the outcome of close binary evolution. Excluding those objects, the average mass becomes 0.609 M., with a dispersion of 0.157 M.. When combining with the sample studied by Bergeron, Saffer, & Liebert (1992), this leads to a set of 164 white dwarfs for which atmospheric parameters and masses have been obtained in a homogeneous way. In this sample 15 objects have M < 0.4 M., thus confirming that about 10% of catalog white dwarfs are helium white dwarfs produced in close binaries. The implications for the stellar initial mass-final mass relation are then discussed in some detail. Some individual objects of particular astrophysical interest are also briefly discussed.