  We extend our recent work on black hole spin in X-ray binary systems to
include an analysis of 189 archival NuSTAR observations from 24 sources. Using
self-consistent data reduction pipelines, spectral models, and statistical
techniques, we report an unprecedented and uniform sample of 36 stellar-mass
black hole spin measurements based on relativistic reflection. This treatment
suggests that prior reports of low spins in a small number of sources were
generally erroneous: our comprehensive treatment finds that those sources tend
to harbor black holes with high spin values. Overall, within $1\sigma$
uncertainty, $\sim86\%$ of the sample are consistent with $a \geq 0.95$,
$\sim94\%$ of the sample are consistent with $a\geq 0.9$, and $100\%$ is
consistent with $a\geq 0.7$ (the theoretical maximum for neutron stars; $a =
cJ/GM^{2}$). We also find that the high-mass X-ray binaries (those with A-, B-,
or O-type companions) are consistent with $a\geq 0.9$ within the $1\sigma$
errors; this is in agreement with the low-mass X-ray binary population and may
be especially important for comparisons to black holes discovered in
gravitational wave events. In some cases, different spectra from the same
source yield similar spin measurements but conflicting values for the
inclination of the inner disk; we suggest that this is due to variable disk
winds obscuring the blue wing of the relativistic Fe K emission line. We
discuss the implications of our measurements, the unique view of systematic
uncertainties enabled by our treatment, and future efforts to characterize
black hole spins with new missions.
