  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.
