We present improved black hole masses for 35 active galactic nuclei (AGNs) based on a complete and consistent reanalysis of broad emission-line reverberation-mapping data. From objects with multiple line measurements, we find that the highest precision measure of the virial product is obtained by using the cross-correlation function centroid (as opposed to the cross-correlation function peak) for the time delay and the line dispersion (as opposed to full width half maximum) for the line width and by measuring the line width in the variable part of the spectrum. Accurate line-width measurement depends critically on avoiding contaminating features, in particular the narrow components of the emission lines. We find that the precision (or random component of the error) of reverberation-based black hole mass measurements is typically around 30%, comparable to the precision attained in measurement of black hole masses in quiescent galaxies by gas or stellar dynamical methods. Based on results presented in a companion paper by Onken et al., we provide a zero-point calibration for the reverberation-based black hole mass scale by using the relationship between black hole mass and host-galaxy bulge velocity dispersion. The scatter around this relationship implies that the typical systematic uncertainties in reverberation-based black hole masses are smaller than a factor of three. We present a preliminary version of a mass-luminosity relationship that is much better defined than any previous attempt. Scatter about the mass-luminosity relationship for these AGNs appears to be real and could be correlated with either Eddington ratio or object inclination. Comment: 61 pages, including 8 Tables and 16 Figures. Accepted for publication in The Astrophysical Journal