There are a total of 157 types of dog breeds recognized by the AKC (American Kennel Club). The names of dog breeds are separated into different dog types which are referred to as Dog Groups.
There are over 150 recognized breeds. New breeds are being made all of the time. Some recent ones are the labradoodle a lab poodle cross and the puggle a pug beagle cross. You can find more information here: akc.org