  We present a uniform analysis of the integrated profile of the H I emission
line of 29,958 nearby ($z < 0.06$) galaxies extracted from the ALFALFA 21 cm
survey. We apply the curve-of-growth technique to derive a database of spectral
parameters and robust estimates of their associated uncertainties. Besides the
central velocity and total flux, the main catalog provides new measures of line
width, profile asymmetry, and profile shape. For a subsample of 13,511 galaxies
with optical properties available from the Sloan Digital Sky Survey, we compute
inclination angle-corrected line widths, rotation velocities empirically
calibrated from spatially resolved observations, and dynamical masses based on
H I sizes estimated from the H I mass. To facilitate subsequent scientific
applications of the database, we also compile a number of ancillary physical
properties of the galaxies, including their optical morphology, stellar mass,
and various diagnostics of star formation activity. We use the homogeneous
catalog of H I parameters to examine the statistical properties of profile
asymmetry and shape. Across the full sample, which covers a wide range of
stellar masses and environments, statistically significant H I profile
asymmetry is detected in $\sim 20\%$ of the galaxy population. The global H I
profiles are $35.2 \pm 0.3\%$ single-peaked, $26.9 \pm 0.3\%$ flat-topped, and
$37.9 \pm 0.3\%$ double-horned. At a given inclination angle, double-horned
profiles are preferentially associated with galaxies of higher stellar mass or
optical concentration, while galaxies of lower mass or concentration tend to
have single-peaked profiles.
