A mixedbreed dog is a member of the world's canine majority; a domestic dog that is not purebred. These dogs are called other names, such as mongrel the formal, traditional term that is often taken to be derogatory these days, and mutt, a slang term often used affectionately. Even so, the old adage that a mixed-breed dog contains the best of all dogs has truth in it, and these dogs are among the most intelligent, healthy, and companionable dogs of all. In recent years, mixed breed or hybrid breed dogs are actually breed on purpose as designer dog, a term causing controversy and often outright hostility among the hobbyists of dog fancy].
The difference between a Mixed-Breed dog and a Purebred dog is more than simply being recognized by a kennel club, it is a genetic one. Purebred dogs tend to be homozygous at most loci, whereas mixed-breeds are heterozygous at many of the loci that determine appearance. This is why purebred dogs will look very similar to their parents but mixed breed dogs will often give puppies of very different appearance even within the same litter. (see dihybrid cross and Mendelian Genetics for more information.)
In creating a mixed-breed dog by mating two different purebreds, the puppies from the litter will look very similar to one another. In genetic terms, they are F1 hybrids; heterozygous at all loci that differed between the two parent breeds. If two F1 hybrids are then mated to one another each of the next generation (F2) of pups will be homozygous at some loci and heterozygous at others (which will be different for each pup). However, after approximately 20 or more generations of crossing the offspring of each generation to one another, with occasional outcrosses to avoid the harmful effects of inbreeding, a new true-breeding line of dogs are produced. This is the basic method from which purebred dogs were created (i.e. they were derived from mixed-breed dogs).
With the long-time popularity of the "breed" name cockapoo, used since at least 1970 and constructed by combining elements of its two contributing breeds (Cocker Spaniel/Poodle), it has become extremely common to find mixed-breed dogs named with breed names likewise invented by portmanteau. The tendency for using such names in a jocular way dates back at least to Queen Elizabeth's Dorgis (Dachshund/Corgi). However, extremely few of these become mainstream "breeds" over long periods with determined breeders, and, as of 2007, Cockapoo and Labradoodle are still the only such combined names to make it into the dictionary. Nonetheless, names such as these commonly appear in for-sale ads and often lack consistency; a cross between a Maltese Terrier and a Poodle, for example, may be advertised as either a "Maltipoo" or a "Moodle".
See the catalogues at Mixed-breed dog/catalogs for lists of popular crosses and their names and nicknames.