  We analyze photometric data in V and I for the globular cluster (GC) systems
in five of the giant ellipticals in the Coma Cluster: NGC 4874, 4881, 4889,
4926, and IC 4051. We find that the GC luminosity functions are quite similar
to one another, with a turnover derived from a composite sample of more than
9,000 GCs at V = 27.71 +- 0.07 (M_V = -7.3). Both a simple Gaussian curve and
an evolved Schechter function fit the bright half of the GCLF equally well,
though the Coma GCLF is broader and has a higher ``cutoff mass'' (M_c ~ 3 x
10^6 M_Sun) than in any of the Virgo giants. These five Coma members exhibit a
huge range in GC specific frequency, from a low of S_N = 0.7 for NGC 4881 up to
12 for IC 4051 and NGC 4874. No single formation scenario appears able to
account for these differences in otherwise-similar galaxies. The supergiant NGC
4874 has the richest globular cluster system known, probably holding more than
30,000 clusters; its true extent is not yet determined and may extend well out
into the Coma potential well. For the three biggest GC systems (NGC 4874, 4889,
IC 4051), all three populations are dominated by red, metal-rich clusters.
Their metallicity distributions also may all have the normal bimodal form, with
the two sequences at the expected mean colors <V-I>(blue) = 0.98 and <V-I>(red)
= 1.15. However, the color distributions and relative numbers of metal-rich
clusters show intriguing counterexamples to a trend established by Peng et al.
2008 (ApJ 681, 197) for the Virgo galaxies. At the very highest-density and
most massive regimes represented by the Coma supergiants, formation of
metal-rich clusters seems to have been especially favored.
