  We present stellar velocity dispersion profiles for seven Milky Way dwarf
spheroidal (dSph) satellite galaxies. We have measured 8394 line-of-sight
velocities (+/- 2.5 km/s) for 6804 stars from high-resolution spectra obtained
at the Magellan and MMT telescopes. We combine these new data with previously
published velocities to obtain the largest available kinematic samples, which
include more than 5500 dSph members. All the measured dSphs have stellar
velocity dispersion of order 10 km/s that remains approximately constant with
distance from the dSph center, out to and in some cases beyond the radius at
which the mean surface brightness falls to the background level. Assuming dSphs
reside within dark matter halos characterized by the NFW density profile, we
obtain reasonable fits to the empirical velocity dispersion profiles. These
fits imply that, among the seven dSphs, M_vir ~ 10^[8-9] M_sun. The mass
enclosed at a radius of 600 pc, the region common to all data sets, ranges from
(2-7) x 10^7 M_sun .
