Unlike humans, dogs are capable of producing their own vitamin C, so supplementation is not necessary.

Raw fed dogs also get vitamin C from liver, kidney, heart and fish.
http://www.kaossiberians.com/old kaos pages/health/Nutrients.pdf

 

There is some anecdotal evidence of vitamin C helping dogs with joint issues, perhaps because of it's antioxidant effects. Like Gally said, dogs synthesize their own vitamin C. If one chooses to supplement with it, it needs to be ester-c, as this is more readily absorbed. It can cause GI upset and diarrhea.