I do not give my boys supplements. If a dog food is labeled "complete and balanced," according to AAFCO guidelines, it is supposed to contain all of the nutrients a dog needs:
Dog Food Standards by the AAFCO
I would consider giving supplements for bone and joint health, glucosamine and chondroitin, but I haven't done it yet. There are lots of supplement choices for skin and hair.
I am concerned about the number of pet specialty shops that are expanding their vitamin and supplement inventory because these items have a high profit margin. Pet owners should never give these things without consulting a vet or nutritionist first. It is too easy to make your pet sick.