That depends, Shannon. While the ripe tubers are not considered to be toxic, the green parts are. Potatoes and other Solanum species, including the tomato, are members of the nightshade family of plants. These plants contain solanine and other toxic alkaloids which, if eaten in large enough amounts, can produce drooling, severe gastrointestinal upset, including vomiting and diarrhea, loss of appetite, drowsiness, central nervous system depression, confusion, behavioral changes, weakness, dilated pupils and slowed heart rate. Therefore, a bit of ripe potato here and there shouldn’t cause any problems for your dogs, but you should be careful that they do not consume the rest of the plant.