There are some disagreements as to whether a vegetarian diet is safe for dogs. A study done by PETA, however, showed that dogs on meatless diets tended to develop less health problems than those who eat meat regularly. Like humans, dogs need a variety of nutrients, so if daily needs are checked, dogs could go on vegetarian diets. They need 22% protein in their daily diet and there are plenty of sources besides meat.

Don't forget to stock up on foods high in protein and vitamins to avoid any deficiencies. Meat isn't really a necessary part of the diet. You can substitute with other products! Check the labels when purchasing food to make sure your pet is received the recommended amount of nutrients and vitamins. ;)

The research points to yes.  There is a comprehensive book about vegetarian dog diets, and their site has a ton of info about it too.

The quick answer is yes, but you should talk to your vet before changing your dog's diet to learn how to safely transition him and also to make sure you are meeting all of your dog's health needs.