We present a statistical study of the properties of faint galaxies from a large catalog of about 13,500 objects found in 112 random fields observed with the Hubble Space Telescope Wide Field Camera before refurbishment. The majority of the objects are faint galaxies with 18 < I < 25 mag. For each object we determine half-light radius, magnitude, color, and a crude classification based on the object's luminosity profile, by fitting two-dimensional models to undeconvolved images. The catalog is better than 80% complete to a depth ranging between I similar to 21 mag for the shortest exposures (0.5 hr), up to 23.8 for the longest exposure (about 5 hr). Number counts in the range 18 < I < 22 mag exceed ground-based results by about 50%; many galaxies in this magnitude range are small enough that they could be misclassified as stars from the ground. A clear bifurcation is found in the observed colors of faint spirals and ellipticals, with the latter becoming significantly redder for I > 20 mag. Typical half-light radii of faint galaxies are somewhat smaller than spirals. Half-light radius is not correlated with (V-I) color for I less than or similar to 21 mag; at fainter magnitudes, a weak correlation in the sense of larger galaxies being redder is marginally detected.