We present a detailed analysis of 108 helium-line (DB) white dwarfs based on model atmosphere fits to high signal-to-noise optical spectroscopy. We derive a mean mass of 0.67M(circle dot) for our sample, with a dispersion of only 0.09M(circle dot). White dwarfs also showing hydrogen lines, the DBA stars, comprise 44% of our sample, and their mass distribution appears similar to that of DB stars. As in our previous investigation, we find no evidence for the existence of low-mass (M < 0.5M(circle dot)) DB white dwarfs. We derive a luminosity function based on a subset of DB white dwarfs identified in the Palomar-Green Survey. We show that 20% of all white dwarfs in the temperature range of interest are DB stars, although the fraction drops to half this value above T-eff similar to 20,000 K. We also show that the persistence of DB stars with no hydrogen features at low temperatures is difficult to reconcile with a scenario involving accretion from the interstellar medium, often invoked to account for the observed hydrogen abundances in DBA stars. We present evidence for the existence of two different evolutionary channels that produce DB white dwarfs: the standard model where DA stars are transformed into DB stars through the convective dilution of a thin hydrogen layer and a second channel where DB stars retain a helium atmosphere throughout their evolution. We finally demonstrate that the instability strip of pulsating V777 Her white dwarfs contains no non-variables, if the hydrogen content of these stars is properly accounted for.