We present an analysis of a 50 orbit HST ACS observation of the M87 globular cluster system. We use the extraordinary depth of this dataset to test whether the colors and magnitudes show evidence for a mass-metallicity relation in globular cluster populations. We find only a weak or absent relation between the colors and magnitudes of the metal poor subpopulation of globular clusters. The weakness or absence of a color-magnitude relation is established over a wide range in luminosity from $M_V=-11$ to $M_V=-6$, encompassing most of the M87 globular clusters. The constancy of the colors of the metal-poor subpopulation seen in our 50 orbit observation is in contrast to suggestions from single orbit ACS data that the metal-poor globular clusters in M87 and several other galaxies show a blue tilt. The formal best fit for the mass-metallicity relation for the metal-poor subpopulation in our much deeper data is $Zpropto M^{0.08pm0.05}$. Our analysis of these data also shows a possible small red tilt in the metal-rich globular cluster subpopulation. While either of these small tilts may be real, they may also illustrate the limit to which mass-metallicity relations can be determined, even in such extraordinarily deep data. We specifically test for a wide range of systematic effects and find that while small tilts cannot be confirmed or rejected, the data place a strong upper limit to any tilt of $|0.20|pm0.05$. This upper limit is much smaller than some earlier claims from single orbit data, and strongly limits self-enrichment within globular clusters. This mass-metallicity relation for globular clusters is also shallower than the relation for galaxies, suggesting that the formation mechanisms for these two types of objects are different.
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