  We present the Stagger-grid, a comprehensive grid of time-dependent, 3D
hydrodynamic model atmospheres for late-type stars with realistic treatment of
radiative transfer, covering a wide range in stellar parameters. This grid of
3D models is intended for various applications like stellar spectroscopy,
asteroseismology and the study of stellar convection. In this introductory
paper, we describe the methods used for the computation of the grid and discuss
the general properties of the 3D models as well as their temporal and spatial
averages (<3D>). All our models were generated with the Stagger-code, using
realistic input physics for the equation of state (EOS) and for continuous and
line opacities. Our ~220 grid models range in Teff from 4000 to 7000K in steps
of 500K, in log g from 1.5 to 5.0 in steps of 0.5 dex, and [Fe/H] from -4.0 to
+0.5 in steps of 0.5 and 1.0 dex. We find a tight scaling relation between the
vertical velocity and the surface entropy jump, which itself correlates with
the constant entropy value of the adiabatic convection zone. The range in
intensity contrast is enhanced at lower metallicity. The granule size
correlates closely with the pressure scale height sampled at the depth of
maximum velocity. We compare the <3D> models with widely applied 1D models, as
well as with theoretical 1D hydrostatic models generated with the same EOS and
opacity tables as the 3D models, in order to isolate the effects of using
self-consistent and hydrodynamic modeling of convection, rather than the
classical mixing length theory approach. For the first time, we are able to
quantify systematically over a broad range of stellar parameters the
uncertainties of 1D models arising from the simplified treatment of physics, in
particular convective energy transport. In agreement with previous findings, we
find that the differences can be significant, especially for metal-poor stars.
