We analyze deep Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) images in U, B, V, I using artificial neural network (ANN) classifiers, which are based on galaxy surface brightness and light profile (but not on color nor on scale length, r(hl)). The ANN distinguishes quite well between E/SO, Sabc, and Sd/Irr+M galaxies (M for merging systems) for B-J less than or similar to 27 mag. We discuss effects from the cosmological surface brightness (SB) dimming and from the redshifted UV morphology on the classifications, and we correct for the latter. We present classifications in UBVI from (a) four independent human classifiers; (b) ANNs trained on V-606 and I-814 images; and (c) an ANN trained on images in the rest-frame UBV according to the expected redshift distribution as a function of B-J. For each of the three methods, we find that the fraction of galaxy types does not depend significantly on wavelength, and that they produce consistent counts as a function of type. The median scale length at B-J similar or equal to 27 mag is r(hl) similar or equal to 0 ''.25-0 ''.3 (1-2 kpc at z approximate to 1-2). fariy- and late-type galaxies are fairly well separated in BM color-magnitude diagrams for B less than or similar to 27 mag, with E/SO galaxies being the reddest and Sd/Irr+M galaxies generally blue. We present the B-band galaxy counts for five WFPC2 fields as a function of morphological type for B-J less than or similar to 27 mag. E/SO galaxies are only marginally above the no-evolution predictions, and Sabc galaxies are at most 0.5 dex above the nonevolving models for B-J greater than or similar to 24 mag. The faint blue galaxy counts in the B band are dominated by Sd/Irr+M galaxies and can be explained by a moderately steep local luminosity function (LF) undergoing strong luminosity evolution. We suggest that these faint late-type objects (24 mag less than or similar to B-J less than or similar to 28 mag) are a combination of low-luminosity lower redshift dwarf galaxies, plus compact star-forming galaxies and merging systems at z similar or equal to 1-3, possibly the building blocks of the luminous early-type galaxies seen today.