Active galaxies are thought to be both fueled and obscured by neutral gas r
emoved from the host galaxy and funneled into a central accretion disk. We
performed a VLA imaging survey of 21 cm absorption in Seyfert and starburst
nuclei to study the neutral gas in the near-nuclear environment. With the
exception of NGC 4151, the absorbing gas traces 100 pc-scale, rotating disk
s aligned with the outer galaxy disk. These disks appear to be rich in atom
ic gas relative to nuclear disks in nonactive spirals. We find no strong ev
idence for rapid infall or outflow of neutral hydrogen, but our limits on t
he mass infall rates are compatible with that required to feed a Seyfert nu
cleus. Among the galaxies surveyed here, neutral hydrogen absorption traces
parsec-scale gas only in NGC 4151. Based on the kinematics of the absorpti
on line, the disk symmetry axis appears to align with the radio jet axis ra
ther than the outer galaxy axis. The most surprising result is that we dete
ct no 21 cm absorption toward the central radio sources of the hidden Seyfe
rt 1 nuclei Mrk 3, Mrk 348, and NGC 1068. Moreover, 21 cm absorption is com
monly observed toward extended radio jet structure but appears to avoid cen
tral, compact radio sources in Seyfert nuclei. To explain these results, we
propose that 21 cm absorption toward the nucleus is suppressed by either f
ree-free absorption, excitation effects (i.e., enhanced spin temperature),
or rapid motion in the obscuring gas. Ironically, the implications of these
effects is that the obscuring disks must be small, typically not larger th
an a few tens of parsecs.