We have conducted a sensitive search for Galactic high-velocity 21 cm
H I clouds along and near the sight lines to quasars. The 5 a complete
ness limit is N-H = 7 x 10(17) cm(-2) which is a factor of 3 more sens
itive than other recent surveys. Approximately 37% of the observed dir
ections show high-velocity gas at \V-LSR\ > 100 km s(-1), excluding th
at which can be associated with the Galactic warp. This is a significa
nt increase in the sky-covering factor above the 18% derived from prev
ious studies. Virtually all of the newly detected emission is associat
ed with previously known high-velocity cloud (HVC) complexes; there is
no evidence for a large population of low column density clouds not a
ssociated with the complexes. HVC complexes appear to be surrounded by
extensive low column density, neutral envelopes. The large observed c
overing factor for Galactic HVCs may have important implications for t
he hypothesis that large gaseous halos are responsible for many of the
narrow metal-line absorption systems seen in the spectra of quasars.