We report on the interaction of water molecules with polar and nonpolar stoichiometric surfaces of cubic silicon carbide, as described by ab initio molecular dynamics at finite temperature. Our calculations show that, irrespective of coverage, in the gas phase water spontaneously dissociates on both polar Si-terminated (001) and nonpolar (110) surfaces, following similar mechanisms. The specific geometric arrangement of atoms on the outermost surface layer is responsible for water orientation and coordination and thus plays a major role in determining surface reactivity. This is found to be the case also for water on a computer-generated amorphous-SiC surface. In addition, from a macroscopic standpoint, the ability of the two crystalline surfaces with different polarities to induce water dissociation can be related to the similarities of their ionization potentials.