A subset of 150 globular clusters (GCs) in M87 has been selected for abundance and age determinations from the 1997 sample of Cohen & Ryzhov. This has been done solely on the basis of the signal-to-noise ratios of the spectra. Indices that measure the strength of the strongest spectral features were determined for the M87 GCs and from new data for twelve galactic GCs. Combining the new and existing data for the galactic GCs and comparing the (U-R) colors and the line indices gave qualitative indications for the ages and abundances of the M87 GC system. Quantitative results, which confirm and extend the qualitative ones, were obtained by applying the Worthey models for the integrated light of stellar systems of a single age, calibrated by observations of galactic globular clusters, to deduce abundances and ages for the objects in our sample. We find that the M87 GCs span a wide range in metallicity, from very metal-poor to somewhat above solar metallicity. The mean [Fe/H] of -0.95 dex is higher than that of the galactic GC system, and there is a metal-rich tail that reaches to higher [Fe/H] than one finds among the galactic GCs. Excluding the very metal-rich tail, there is marginal evidence for a bimodal distribution over the single one at the 89% significance level. The two subpopulations in this model are located at -1.3 and -0.7 dex and contain 40% and 60% of the total, respectively. The dispersion in [Fe/H] for each of the model subpopulations is σ = 0.3 dex. The mean metallicity of the M87 GC system is about a factor of 4 lower than that of the M87 stellar halo at a fixed projected radius R. The metallicity inferred from the X-ray studies is similar to that of the M87 stellar halo, not to that of the M87 GC system. We infer the relative abundances of Na, Mg, and Fe in the M87 GCs from the strength of their spectral features. The behavior of these elements between the metal-rich and metal-poor M87 GCs is similar to that shown by the galactic GCs and by halo stars in the Galaxy. The pattern of chemical evolution in these disparate old stellar systems is, as far as we can tell, identical. Superposed on a very large dispersion in abundance at all R, there is a small but real radial gradient in the mean abundance of the M87 GCs with R, but no detectable change in the Hβ index with R. We obtain a median age for the M87 GC system of 13 Gyr, similar to that found for the galactic GCs. The dispersion about that value (σ = 2 Gyr) is small.