In the Spring of 2011 we carried out a 2.5 month reverberation mapping campaign using the 3 m Shane telescope at Lick Observatory, monitoring 15 low-redshift Seyfert 1 galaxies. This paper describes the observations, reductions and measurements, and data products from the spectroscopic campaign. The reduced spectra were fitted with a multicomponent model in order to isolate the contributions of various continuum and emission-line components. We present light curves of broad emission lines and the AGN continuum, and measurements of the broad H-beta line widths in mean and root-mean square (rms) spectra. For the most highly variable AGNs we also measured broad H-beta line widths and velocity centroids from the nightly spectra. In four AGNs exhibiting the highest variability amplitudes, we detect anticorrelations between broad H-beta width and luminosity, demonstrating that the broad-line region breathes on short timescales of days to weeks in response to continuum variations. We also find that broad H-beta velocity centroids can undergo substantial changes in response to continuum variations; in NGC 4593 the broad H-beta velocity shifted by ~250 km/s over a one-month duration. This reverberation-induced velocity shift effect is likely to contribute a significant source of confusion noise to binary black hole searches that use multi-epoch quasar spectroscopy to detect binary orbital motion. We also present results from simulations that examine biases that can occur in measurement of broad-line widths from rms spectra due to the contributions of continuum variations and photon-counting noise.