We present a detailed investigation of neutron star atmospheres with low magnetic fields, B<~10^8^-10^10^G, which do not affect opacities and equation of state of the atmospheric matter. We compute the atmospheric structure, emergent spectral fluxes and specific intensities for hydrogen, helium and iron atmospheres in a wide domain of effective temperatures and gravitational accelerations expected for neutron stars. The iron atmospheres are computed with the opacities and equations of state from the OPAL opacity library. We show that the model atmosphere spectra are substantially different from the blackbody spectra. For light element atmospheres, the flux is greater than the blackbody flux, and the spectrum is harder, at high photon energies, whereas at low energies the spectral flux follows the Rayleigh-Jeans law with a (surface) temperature lower than the effective temperature. The spectra of iron atmospheres display prominent spectral features in the soft X-ray range. The emergent specific intensity is anisotropic, with the anisotropy depending on energy. These properties of the atmospheric radiation should be taken into account for the proper interpretation of the thermal component of the neutron star radiation detectable at X-ray through UV energies. In particular, fitting of the thermal component with the blackbody model may result in substantially incorrect parameters of the radiating regions. We discuss an application of our atmosphere models to the nearby millisecond pulsar PSR J0437-4715.