The evolution of the neutral hydrogen content of galaxies as a function of time is an important constraint on processes in galactic evolution. We present a comprehensive, statistical description of the H I content and distribution within galaxies at the present epoch and compare these statistics with the properties of H I associated with "damped Lyα" absorption systems at high redshift that are observed in the spectra of QSOs. ΩH I(z = 0), the H I mass density at the present epoch relative to the present critical mass density, is found to be (2.5±0.6) × 10-4h-175, consistent with the decreasing trend of the H I content with time deduced from QSO absorption line statistics for redshifts from about 4 to 0.5 (Lanzetta 1993). Spiral galaxies contain an overwhelming 89% of this neutral hydrogen mass. The rest is contained in irregulars, SOs, and ellipticals Spirals also offer the largest cross section to line-of-sight absorption of light from QSOs By considering nearby spirals as potential absorbers, the interception probability as a function of the H I column density, N(H I), is derived for comparison with the cross sections inferred from observations of damped Lyman-alpha systems. The comparison shows that the damped Lyα lines are created by absorbers that subtend larger cross sections than present-day spirals by a factor of 5 implying that galaxies were either larger or more numerous at z ∼ 2.5.