We have used the high-resolution camera at the Canada-France-Hawaii Telescope to obtain VRI photometry of the globular clusters in the innermost 140 of the M87 halo. The results are used to discuss several issues concerning the formation and evolution of globular cluster systems in supergiant elliptical galaxies like M87. Our principal results are as follows: (1) From our deep R-band photometry of the cluster population, we find no significant change in the globular cluster luminosity function (GCLF) with galactocentric radius, for cluster masses M>=10^5^M_{sun}_. This result places constraints on current theoretical predictions of the rate of cluster evolution by tidal shocking and evaporation, indicating that the main effects of dynamical evolution may be felt only on lower mass clusters (~5, distinctly earlier than most other galaxies.