  Our current understanding of the stellar initial mass function and massive
star evolution suggests that young globular clusters may have formed hundreds
to thousands of stellar-mass black holes, the remnants of stars with initial
masses from $\sim 20 - 100\, M_\odot$. Birth kicks from supernova explosions
may eject some black holes from their birth clusters, but most should be
retained. Using a Monte Carlo method we investigate the long-term dynamical
evolution of globular clusters containing large numbers of stellar black holes.
We describe numerical results for 42 models, covering a range of realistic
initial conditions, including up to $1.6\times10^6$ stars. In almost all models
we find that significant numbers of black holes (up to $\sim10^3$) are retained
all the way to the present. This is in contrast to previous theoretical
expectations that most black holes should be ejected dynamically within a few
Gyr. The main reason for this difference is that core collapse driven by black
holes (through the Spitzer "mass segregation instability") is easily reverted
through three-body processes, and involves only a small number of the most
massive black holes, while lower-mass black holes remain well-mixed with
ordinary stars far from the central cusp. Thus the rapid segregation of stellar
black holes does not lead to a long-term physical separation of most black
holes into a dynamically decoupled inner core, as often assumed previously.
Combined with the recent detections of several black hole X-ray binary
candidates in Galactic globular clusters, our results suggest that stellar
black holes could still be present in large numbers in many globular clusters
today, and that they may play a significant role in shaping the long-term
dynamical evolution and the present-day dynamical structure of many clusters.
