We have recently completed a 64-night spectroscopic monitoring campaign at the Lick Observatory 3 m Shane telescope with the aim of measuring the masses of the black holes in 12 nearby (z < 0.05) Seyfert 1 galaxies with expected masses in the range ∼ 106-107 M ⊙ and also the well-studied nearby active galactic nucleus (AGN) NGC5548. Nine of the objects in the sample (including NGC5548) showed optical variability of sufficient strength during the monitoring campaign to allow for a time lag to be measured between the continuum fluctuations and the response to these fluctuations in the broad Hβ emission, which we have previously reported. We present here the light curves for the Hα, Hγ, He II λ4686, and He I λ5876 emission lines and the time lags for the emission-line responses relative to changes in the continuum flux. Combining each emission-line time lag with the measured width of the line in the variable part of the spectrum, we determine a virial mass of the central supermassive black hole from several independent emission lines. We find that the masses are generally consistent within the uncertainties. The time-lag response as a function of velocity across the Balmer line profiles is examined for six of the AGNs. We find similar responses across all three Balmer lines for Arp151, which shows a strongly asymmetric profile, and for SBS1116+583A and NGC6814, which show a symmetric response about zero velocity. For the other three AGNs, the data quality is somewhat lower and the velocity-resolved time-lag response is less clear. Finally, we compare several trends seen in the data set against the predictions from photoionization calculations as presented by Korista & Goad. We confirm several of their predictions, including an increase in responsivity and a decrease in the mean time lag as the excitation and ionization level for the species increases. Specifically, we find the time lags of the optical recombination lines to have weighted mean ratios of τ(Hα):τ(Hβ):τ(Hγ):τ(He I):τ(He II) = 1.54:1.00:0.61:0.36:0.25. Further confirmation of photoionization predictions for broad-line gas behavior will require additional monitoring programs for these AGNs while they are in different luminosity states. © 2010. The American Astronomical Society. All rights reserved.