What types of vitamins should dogs take?

It really depends of what you are trying to achieve with your dog, ie a glossy coat or heathy joints. Admittedly the majority of supplements for dogs are focused around healthy joints so I will assume this is the type of supplements you are looking for.

If this is the case you should look for a supplement containing glucosamine and chondroitin, preferably one that is being used and recommend by vet's. Have a look at www.dog-pain-relief.org. The guy who made it has videos from vets about supplements and recommends a supplement for dogs joints.