Using a new spectroscopic sample and methods accounting for spectroscopic sampling fractions that vary in magnitude and surface brightness, we present R-band galaxy luminosity functions (GLFs) for six nearby galaxy clusters with redshifts of 4000 km s^-1 < cz < 20,000 km s^-1 and velocity dispersions of 700 km s^-1 < σ < 1250 km s^-1. In the case of the nearest cluster, A1060, our sample extends to M_R = -14 (7 mag below M*), making this the deepest spectroscopic determination of the cluster GLF to date. Our methods also yield composite GLFs for cluster and field galaxies to M_R = -17 (M* + 4), including the GLFs of subsamples of star-forming and quiescent galaxies. The composite GLFs are consistent with Schechter functions (M = -21.14, α = -1.21 for the clusters, M = -21.15, α = -1.28 for the field). All six cluster samples are individually consistent with the composite GLF down to their respective absolute magnitude limits, but the GLF of the quiescent population in clusters is not universal. There are also significant variations in the GLF of quiescent galaxies between the field and clusters that can be described as a steepening of the faint-end slope. The overall GLF in clusters is consistent with that of field galaxies, except for the most luminous tip, which is enhanced in clusters versus the field. The star formation properties of giant galaxies are more strongly correlated with the environment than those of fainter galaxies.