Density-functional theory calculations of the LiNbO3 (21̅ 1̅ 0), (11̅ 00), and (0001) surfaces, commonly referred to as X, Y, and Z cuts, are presented. In case of the Z cut, we find a pronounced dependence of the surface structure and stoichiometry on the direction of the ferroelectric polarization. In contrast, the influence of the chemical potentials of the surface constituents is limited. Rather electrostatics governs the surface stability. Different from the Z cut, the stoichiometry of the X cut and Y cut is clearly dependent on the preparation conditions. The surface charge observed for the nominal nonpolar Y cut is traced back to the formation of a strong surface dipole.