Yes. The human blood group system is based on three different antigen: A, B and O. The possible blood types we could have are A, B, AB and O and each one of these can be either Rh positive or negative. Type O negative blood is generally considered to be universally accepted by any other blood type and type AB positive can receive any other type.
Dog for their part, have more than eight different antigens that can attach to their red blood cells, most of them labeled Dog Erythocyte Antigen (DEA 1.1, 1.2, 3, 4, 5, 6 and 7). Often individuals within a specific breed of dog will have the same blood type - for instance, 60 percent of greyhounds fall into the DEA 1.1 Negative (the universal dog donor) blood group. But new canine blood groups are still being detected- the recently discovered Dal blood group, for example, is only found in Dalmatians.
Cat on the other hand, have only two possible antigens - A and B although they are not the same A and B antigens found on human blood. There is no universal donor or recipient feline blood groups but the vast majority around 90 percent of domestic cats have type A blood, while more exotic purebreds often type B. AB is possible but very rare.
Like dogs, horse blood groups are loosely organized along breed lines, but there are 30 different groups that represent combinations of 8 different antigens A, C, D, K, P, Q and U are internationally recognized, while T is still being researched. Cows are tricky because there are 11 major blood groups A, B, C, F, J, L, M, R,S, T and Z BUT THE b group includes over 60 different antigens making blood matches for transfusion tough.