A first-principles calculation of stacking fault energies in 3C-, 4H-, and 6H-SiC, based on the local-density approximation within the density-functional theory, is reported. All the structurally different stacking faults which can be introduced by glide along the (0001) basal plane are considered. The number of such stacking faults in these polytypes is one, two, and three, respectively. The stacking fault energies are also calculated using the simpler generalized axial next-nearest-neighbor Ising (ANNNI) model. Our calculations confirm that the stacking fault energy of 3C-SiC is negative, and we also find that one of the three types of stacking faults in 6H-SiC has a considerably higher stacking fault energy than the other two types.