According to Dr. Laura Robinson, DVM, there is no credible reason why your dog's diet should not include grains.
The grain-free diet has gained steam from the idea that dogs evolved from wolves, and wolves do not have grains readily available in their diets. However, dogs did indeed evolve, and so did their gastro-intestinal systems which can now handle grain without issue. More recently, grain-free diets have been associated with a cardiac disease called Dilated Cardiomyopathy, a genetic disease that normally effects dobermans and golden retrievers. Veterinarians have noticed an increase in this disease in dogs directly related to grain-free diets and balances of amino acids resulting from lack of taurine.
Some dogs are indeed allergic to grain, in which case they should avoid them, but for the most part, your dog should be perfectly fine ingesting grains.