Well, there are approximately 78 million dogs in the United States. There are over 400 breeds of dogs that do not include mutts and then you have wild dogs like the African Wild Dog, Wolf, Coyote, Dingo, etc.
Additionally there are feral dogs all over the world, that were once pet dogs but have gone wild.
Honestly there is no way of knowing how many dogs there are on the planet. I hope my answer helps some though :)