  The central region of the Virgo cluster of galaxies contains thousands of
globular clusters (GCs), an order of magnitude more than the numbers found in
the Local Group. Relics of early star formation epochs in the universe, these
GCs also provide ideal targets to test our understanding of the Spectral Energy
Distributions (SEDs) of old stellar populations. Based on photometric data from
the Next Generation Virgo cluster Survey (NGVS) and its near-infrared
counterpart NGVS-IR, we select a robust sample of 1846 GCs with excellent
photometry and spanning the full range of colors present in the Virgo core. The
selection exploits the well defined locus of GCs in the uiK diagram and the
fact that the globular clusters are marginally resolved in the images. We show
that the GCs define a narrow sequence in 5-dimensional color space, with
limited but real dispersion around the mean sequence. The comparison of these
SEDs with the predictions of eleven widely used population synthesis models
highlights differences between models, and also shows that no single model
adequately matches the data in all colors. We discuss possible causes for some
of these discrepancies. Forthcoming papers of this series will examine how best
to estimate photometric metallicities in this context, and compare the Virgo
globular cluster colors with those in other environments.
