Like humans dogs benefit from water-soluble vitamins on a daily basis and certain B vitamins such as folate. Your vet may even recommend supplementing your dogs diet with specific fruits and vegetables instead of vitamin supplements according to Dr. Whether this is because your dog is ill or just extremely finicky a multivitamin can help ward off deficiencies in these situations.
If a vitamin is good enough for a human it should be good enough for a dog or cat right. Despite this some dog breeds can benefit from supplementation especially if suffering from joint pains digestive problems and urinary tract issues. Dogs can manufacture their own vitamin C and do not require it in their diet like humans do so the value of supplementing vitamin C remains unclear.
Read the label of any multivitamin product you take to make sure you are aware of what it contains.