  We have searched for radio pulsations towards 49 Fermi Large Area Telescope
(LAT) 1FGL Catalog $\gamma$-ray sources using the Green Bank Telescope at 350
MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data;
10 of these were discoveries unique to our survey. Sixteen are binaries, with
eight having short orbital periods $P_B < 1$ day. No radio pulsations from
young pulsars were detected, although three targets are coincident with
apparently radio-quiet $\gamma$-ray pulsars discovered in LAT data. Here, we
give an overview of the survey and present radio and $\gamma$-ray timing
results for the 10 MSPs discovered. These include the only isolated MSP
discovered in our survey and six short-$P_B$ binary MSPs. Of these, three have
very low-mass companions ($M_c$ $\ll$ 0.1M$_{\odot}$) and hence belong to the
class of black widow pulsars. Two have more massive, non-degenerate companions
with extensive radio eclipses and orbitally modulated X-ray emission consistent
with the redback class. Significant $\gamma$-ray pulsations have been detected
from nine of the discoveries. This survey and similar efforts suggest that the
majority of Galactic $\gamma$-ray sources at high Galactic latitudes are either
MSPs or relatively nearby non-recycled pulsars, with the latter having on
average a much smaller radio/$\gamma$-ray beaming ratio as compared to MSPs. It
also confirms that past surveys suffered from an observational bias against
finding short-$P_B$ MSP systems.
