There are over 500 breeds. All of them are not in the AKC or BKC though. There are around 600 including "designer doggie" breeds (such as a Puggle [pug + beagle] Pomapoo [pomeranian + poodle] and many MANY others. But, if you include ALL mixed breeds, then there is an infinite combination of anywhere from 2 breeds bred together...all the way to over 10s and ...