dogs that dont shed. well this is a little bit of a misconception. poodles, bichons, schnauzers, malteses, etc shed into their coat, meaning the hair just matts, instead of shedding out, it sheds in, so to speak. so while you wont have much of a problem with the hair everywhere, you will have to brush any of these dogs daily, as it takes maybe a day for matts to form on dogs like this.
and to correct, short haired breeds shed a lot.