We have investigated the photorefractive (photoinduced) light scattering in lithium niobate single crystals: LiNbO3, LiNbO3:B, LiNbO3:Y(0.46 mas %), LiNbO3:Y(0.24):Mg(0.63 mas %), and LiNbO3:Ta(1.13):Mg(0.0109 mas %) that were grown from congruent melts. We have found that the shape of the speckle structure of this scattering and the kinetics of the development of its indicatrix depend substantially on the type of the impurity dopant in the lithium niobate crystal. We have observed that, upon laser irradiation of crystals doped with Y3+, Ta5+:Mg2+, and Y3+:Mg2+, the shape of their scattering indicatrix changes with time. At the same time, the LiNbO3:B crystal is characterized by a complete absence of time changes in its speckle structure, which indicates that the photorefractive effect in this crystal is substantially lowered.