Many countries have their own kennel clubs where dog breed owners can register their dog.  Kennel clubs maintain breed standards, record pedigrees, and establish rules for dog shows, dog trials and qualification of judges. If you want to enter your dog in a dog show, it will almost certainly need to be registered in the appropriate kennel club. The oldest kennel club in the world is The Kennel Club in the United Kingdom which was established in 1873.

The best known kennel club in the United States is the American Kennel Club (AKC) founded in 1884. Next oldest is the United Kennel Club (UKC) founded in 1898 in the United States. Most of the most popular dog breeds are recognized by both clubs with only a few exceptions. Dogs included in the AKC can be found here, and those of the UKC, here.  Dogs recognized by the Kennel Club (UK) on on this page.

For English speaking countries, the best known kennel clubs include:

The Fédération Cynologique Internationale (FCI) represents over eighty countries. Standards for dog breeds included in the Foundation Stock Services (AKC) will use FCI standards.

From Wikipedia, the free encyclopedia:

A dog breed is a particular strain or dog type that was purposefully bred by humans to perform specific tasks, such as hl consistently produce the desirable physical traits, movement and temperament that was developed over decades of selective breeding. For each breed they recognize, kennel clubs and breed registries usually maintain and publish a breed standard which is a written description of the ideal specimen of the breed. Other uses of the term breed when referring to dogs include pure breeds, cross-breeds, mixed breeds and natural breeds. Wikipedia