  We have searched for redshifted absorption in the 21 cm line of neutral
hydrogen toward `red quasars', which are extragalactic radio sources with a
steep spectral drop between optical and infrared wavelengths. The success rate
for detecting HI 21cm absorption toward a representative sample of such sources
is 80%. This compares to the much lower success rate of 11% for detecting HI
21cm absorption associated with optically selected Mg II absorption line
systems. The large neutral hydrogen column densities seen toward red quasars
supports the hypothesis that these sources are reddened by dust, as opposed to
having an intrinsically red spectrum due to the AGN emission mechanism. The
lower limits to the spin temperatures for the neutral hydrogen are between 50 K
and 1000 K, assuming a Galactic dust-to-gas ratio. We consider the question of
biases in optically selected samples of quasars due to dust obscuration. The
data on the red quasar sub-sample support the models of Fall and Pei for dust
obscuration by damped Ly alpha absorption line systems, and suggest that: (i)
there may be a significant, but not dominant, population of quasars missing
from optically selected samples due to dust obscuration, perhaps as high as 20%
at the POSS limit for an optical sample with a redshift distribution similar to
the 1 Jy, flat spectrum quasar sample, and (ii) optically selected samples may
miss about half the high column density quasar absorption line systems.
