All puppies make me go awww. But the main breed that makes me AWWW, as puppies and adults, is Basset Hounds and Bloodhounds. Something about those big ears, wrinkles and soft eyes just melts me. I dont think I would ever own either but I think both are some of the cutest dogs.
I also have to awww over a happy, bouncy Papillon. Border Collies are cute but they tend to get an "oooo" out of me.