We analyze the luminosity function of the globular clusters (GCs) belonging to the early-type galaxies observed in the ACS Virgo Cluster Survey. We have obtained estimates for a Gaussian representation of the GC luminosity function (GCLF) for 89 galaxies. We have also fit the GCLFs with an evolved Schechter function, which is meant to reflect the preferential depletion of low-mass GCs, primarily by evaporation due to two-body relaxation, from an initial Schechter mass function similar to that of young massive clusters. We find a significant trend of the GCLF dispersion with galaxy luminosity, in the sense that smaller galaxies have narrower GCLFs. We show that this narrowing of the GCLF in a Gaussian description is driven by a steepening of the GC mass function above the turnover mass, as one moves to smaller host galaxies. We argue that this behavior at the high-mass end of the GC mass function is most likely a consequence of systematic variations of the initial cluster mass function. The GCLF turnover mass M_TO is roughly constant, at ~ 2.2 x 10^5 M_sun in bright galaxies, but it decreases slightly in dwarfs with M_B >~ -18. We show that part of the variation could arise from the shorter dynamical friction timescales in smaller galaxies. We probe the variation of the GCLF to projected galactocentric radii of 20-35 kpc in the Virgo giants M49 and M87, finding that M_TO is essentially constant over these spatial scales. Our fits of evolved Schechter functions imply average dynamical mass losses (Delta) over a Hubble time that fall in the range 2 x 10^5 <~ (Delta/M_sun) < 10^6 per GC. We agree with previous suggestions that if the full GCLF is to be understood in more detail GCLF models will have to include self-consistent treatments of dynamical evolution inside time-dependent galaxy potentials. (Abridged)
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