What would the average of all dogs look like?

To be more specific, if suddenly no one had any interest in maintaining purebred breeds and all dogs  interbred, would certain common features begin to take hold across the species after, say 500 years. Would we eventually have pockets of new, naturally-evolved breeds in certain areas of the world? At what point would the dogs in the US start to become so different from their Icelandic counterparts that they would not be able to produce viable offspring together?