Sorry guys, I will have to agree with Kelsey on this, dogs are natural carnivores and we as humans shouldn't put our personal beliefs on to them to make ourselves feel like we're doing the right thing, by who, by them or by us, because of our eating choices? Not to assume you are doing this of course, but perhaps others are.
Of course I don't doubt there will be the exceptions were dogs do remakably well on a vegetarian diet, but on a whole I think one should be careful in encouraging such a thing as it may not suit all dogs and lead to medical conditions down the track. I do however think it's great that you add vegetables and grains to your dog's food as well as meat, there is definitely no reason why it should be solely meat of course.
And, lastly if you have encountered ignorant folk asking 'well if you're a vegetarian what do you feed your dog or cat?' Just tell them the truth, as your pet does not have choice, we as humans do.