We present and compare in this paper new photometric redshift catalogs of the galaxies in three public fields: the NTT Deep Field, the HDF-N and the HDF-S. Photometric redshifts have been obtained for thewhole sample, by adopting a $χ^2$ minimization technique on a spectral library drawn from the Bruzual and Charlot synthesis models, with the addition of dust and intergalactic absorption. The accuracy, determined from 125 galaxies with known spectroscopic redshifts, is $σ_z∼ 0.08 (0.3)$ in the redshift intervals $z=0-1.5 (1.5-3.5)$. The global redshift distribution of I-selected galaxies shows a distinct peak at intermediate redshifts, z~0.6 at I_{AB}<26 and z~0.8 at I_{AB}<27.5 followed by a tail extending to z~6. We also present for the first time the redshift distribution of the total IR-selected sample to faint limits ($Ks ≤ 21$ and $J≤22$). It is found that the number density of galaxies at 1.25<z<1.5 is ~ 0.1 /arcmin^22 at J<=21 and ~1./arcmin^2} at J<22, and drops to 0.3/arcmin^2 (at J<22) at 1.5<z<2. The HDFs data sets are used to compare the different results from color selection criteria and photometric redshifts in detecting galaxies in the redshift range 3.5<z<4.5 Photometric redshifts predict a number of high z candidates in both the HDF-N and HDF-S that is nearly 2 times larger than color selection criteria, and it is shown that this is primarily due to the inclusion of dusty models that were discarded in the original color selection criteria by Madau et al 1998. In several cases, the selection of these objects is made possible by the constraints from the IR bands. Finally, it is shown that galactic M stars may mimic z>5 candidates in the HDF filter set and that the 4 brightest candidates at $z>5$ in the HDF-S are indeed most likely M stars. (ABRIDGED) Comment: Version accepted on July, 20, 2000. To appear on Astronomical Journal, Nov 2000. The data and photometric redshift catalogs presented here are available on line at http://www.mporzio.astro.it/HIGHZ