In New Zealand it's actually illegal to walk a dog anywhere without a collar. Anytime a dog is off private property it is required to wear a collar and leash. Except for dog exercise areas where a dog is permitted without a leash but with a collar.
I think having a collar is important as it not only carries contact information like your home address but also is an indication that your dog is not a stray and therefore won't be impounded. Collars also make it easier to attach a leash and control your dog if there are children or people afraid of dogs around. Lots of people, one of my grandmothers included are afraid of dogs. As a responsible dog owner one should always be able to manage and control their dog.
