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We report on a large-scale study of the distribution of globular clusters (GCs) throughout the Virgo cluster, based on photometry from the Next Generation Virgo Cluster Survey (NGVS), a large imaging survey covering Virgo's primary subclusters (Virgo A = M87 and Virgo B = M49) out to their virial radii. Using the g_o', (g' - i')_ocolor-magnitude diagram of unresolved and marginally resolved sources within the NGVS, we have constructed two-dimensional maps of the (irregular) GC distribution over 100 deg² to a depth of g_o' = 24. We present the clearest evidence to date showing the difference in concentration between red and blue GCs over the full extent of the cluster, where the red (more metal-rich) GCs are largely located around the massive early-type galaxies in Virgo, while the blue (metal-poor) GCs have a much more extended spatial distribution with significant populations still present beyond 83' (∼215 kpc) along the major axes of both M49 and M87. A comparison of our GC maps to the diffuse light in the outermost regions of M49 and M87 show remarkable agreement in the shape, ellipticity, and boxiness of both luminous systems. We also find evidence for spatial enhancements of GCs surrounding M87 that may be indicative of recent interactions or an ongoing merger history. We compare the GC map to that of the locations of Virgo galaxies and the X-ray intracluster gas, and find generally good agreement between these various baryonic structures. We calculate the Virgo cluster contains a total population of N_GC= 67, 300±14, 400, of which 35% are located in M87 and M49 alone. For the first time, we compute a cluster-wide specific frequency S_N, CL_= 2.8±0.7, after correcting for Virgo's diffuse light. We also find a GC-to-baryonic mass fraction ε_b= 5.7±1.1x10^–4 and a GC-to-total cluster mass formation efficiency ε_t= 2.9±0.5x10^–5, the latter values slightly lower than but consistent with those derived for individual galactic halos. Taken as a whole, our results show that the production of the complex structures in the unrelaxed Virgo cluster core (including the production of the diffuse intracluster light) is an ongoing and continuing process.