Dogs do have blood types. Blood types are classified by the antigens that are found on the surface of red blood cells. Humans have the ABO system because there are three antigens found in the blood. Dogs, on the other hand, have more than eight antigens called dog erythrocyte antigens or DEA. Their blood types are correspondingly labeled DEA 1.1, DEA 1.2, and DEA 3 through 8 - these are the internationally-recognized standard. New antigens have also been discovered forming the newer groups such as Dal, Kai-1, and Kai-2.
Determining the antigens present in your dog's blood is important.
Because most dogs do not have natural antibodies for antigens they're negative of, their first transfusion is usually harmless and they could safely receive blood from most donors.
However, your dog develops an immune response and will recognize foreign antigens on the first transfusion. When they are sensitized to antigens that they do not have, they will attack blood cells that contain those antigens in succeeding transfusions which could cause fatal reactions.