  Very sensitive HI 21cm observations have been made in 860 directions at dec
>= -43deg in search of weak, Galactic, high-velocity HI emission lines at
moderate and high Galactic latitudes. One-third of the observations were made
toward extragalactic objects. The median 4-sigma detection level is NHI =
8x10^{17} cm^-2 over the 21' telescope beam. High-velocity HI emission is
detected in 37% of the directions; about half of the lines could not have been
seen in previous surveys. The median FWHM of detected lines is 30.3 km/s. High-
velocity HI lines are seen down to the sensitivity limit of the survey implying
that there are likely lines at still lower values of NHI. The weakest lines
have a kinematics and distribution on the sky similar to that of the strong
lines, and thus do not appear to be a new population. Most of the emission
originates from objects which are extended over several degrees; few appear to
be compact sources. At least 75%, and possibly as many as 90%, of the lines are
associated with one of the major high-velocity complexes. The Magellanic Stream
extends at least 10 deg to higher Galactic latitude than previously thought and
is more extended in longitude as well. Although there are many lines with low
column density, their numbers do not increase as rapidly as NHI^-1, so most of
the HI mass in the high-velocity cloud phenomenon likely resides in the more
prominent clouds. The bright HI features may be mere clumps within larger
structures, and not independent objects.
