We present a complete morphologically classified sample of 144 faint field galaxies from the HST Medium Deep Survey with 20.0 ≤ mI < 22.0 mag. We compare the global properties of the ellipticals and early- and late-type spirals and find a nonnegligible fraction (13/144) of compact blue [(V-I) ≤ 1.0 mag] systems with r1/4 profiles. We give the differential galaxy number counts for ellipticals and early-type spirals independently and find that the data are consistent with no-evolution predictions based on conventional flat Schechter luminosity functions (LFs) and a standard cosmology. Conversely, late-type/irregulars show a steeply rising differential number count with slope (δ log N/δm) = 0.64 ± 0.1. No-evolution models based on the Loveday et al. and Marzke et al. local luminosity functions underpredict the late-type/irregular counts by 1.0 and 0.5 dex, respectively, at mI = 21.75 mag. Examination of the irregulars alone shows that ∼ 50% appear inert and the remainder have multiple cores. If the inert galaxies represent a nonevolving late-type population, then a Loveday-like LF (α ≃ -1.0) is ruled out for these types, and an LF with a steep faint end (α ≃ -1.5) is suggested. If multiple core structure indicates recent star formation, then the observed excess of faint blue field galaxies is likely a result of evolutionary processes acting on a steep field LF for late-type/irregulars. The evolutionary mechanism is unclear, but 60% of the multiple-core irregulars show close companions. To reconcile a Marzke-like LF with the faint redshift surveys, this evolution must be preferentially occurring in the brightest late-type galaxies with z ≳ 0.5 at mI = 21.75 mag.