  We present the most extensive combined photometric and spectroscopic study to
date of the enormous globular cluster (GC) system around M87, the central giant
elliptical galaxy in the nearby Virgo cluster. Using observations from DEIMOS
and LRIS at Keck, and Hectospec on the MMT, we derive new, precise radial
velocities for 451 GCs around M87, with projected radii from ~ 5 to 185 kpc. We
combine these measurements with literature data for a total sample of 737
objects, which we use for a re-examination of the kinematics of the GC system
of M87. The velocities are analyzed in the context of archival wide-field
photometry and a novel Hubble Space Telescope catalog of half-light radii,
which includes sizes for 344 spectroscopically confirmed clusters. We use this
unique catalog to identify 18 new candidate ultra-compact dwarfs, and to help
clarify the relationship between these objects and true GCs.
  We find much lower values for the outer velocity dispersion and rotation of
the GC system than in earlier papers, and also differ from previous work in
seeing no evidence for a transition in the inner halo to a potential dominated
by the Virgo cluster, nor for a truncation of the stellar halo. We find little
kinematical evidence for an intergalactic GC population. Aided by the precision
of the new velocity measurements, we see significant evidence for kinematical
substructure over a wide range of radii, indicating that M87 is in active
assembly. A simple, scale-free analysis finds less dark matter within ~85 kpc
than in other recent work, reducing the tension between X-ray and optical
results. In general, out to a projected radius of ~ 150 kpc, our data are
consistent with the notion that M87 is not dynamically coupled to the Virgo
cluster; the core of Virgo may be in the earliest stages of assembly.
