Note that some breeds have a link to their official breed registry websites.

Light Horses:
Quarter horse
Arabian
Spanish Barb
Anglo-Arab
Paint
Appaloosa
American Warmblood
Canadian Warmblood
Dutch Warmblood
Swiss Warmblood
Knabstrup
Gelderlander
Trakehner
Irish Thoroughbred
Thoroughbred
Lusitano
Shagya Arabian
Rocky Mountain Horse
Missori Fox Trotter
Tennesse Walker
Mustang
Palimino
Albino
Morgan
Hispano
Persian Arab
Andalusian
Carthusian
Alter-Real
Cleveland Bay
Hackney
Irish Hunter
Irish Cob
French Trotter
Standeredbred
French Anglo-Arab
Selle Francias
Maremmana
Murgese
Sardinian Anglo-Arab
Salerno
Calabrese
Sicilian
Welsh Cob
Frederiksberg
San Fratello
Oldenburg
Hanoverian
Holstein
WÜrttemberg
East Friesian
Mecklenburg
Lipizzaner
Swedish Warm-blood
Gidran Arabian
Nonius
Furioso-North Star
East Bulgarian
Pleven
Danubian
Malapolski
Wielkopolski
Akhal-Teke
Don
Budyonny
Iomud
Turkoman
Metis Trotter
Orlov
Novokirghiz
Ukranian Riding Horse
Tersky
Karabair
Kabardin
Karabakh
Lokai
Toric
Latvian
Kustanair
Karacabey
Pinto
American Saddlebred
Wild Horse of Wyoming
Canadian Cutting Horse
Azteca
Paso Fino
Criollo
Waler
Brumby

Heavy Drafts:
Friesian
Belgian
Brabant
Percheron
Shire
Clydesdale
Boulonnais
Comtois
Breton
Auxios
Ardennais
Trait Du Nord
Poitevin
Suffolk Punch
Irish Draft
Dole Gudbrandsdal
North Swedish Horse
Swedish Ardennes
Jutland
Dutch Draft
Schleswig Heavy Draft
Rhineland Heavy Draft
Noriker
Franches-Montagnes
Itailian Heavy Draft
Sokolsky
Murakoz
Soviet Heavy Draft
Russian Heavy Draft
Vladimar Heavy Draft
Lithuanian Heavy Draft

Ponies:
Tarpan
Hucul
Konik
Asiatic Wild Horse
Mongolian
Manipuri
Spiti
Kathiawari and Marwari
Tibetan
Caspian
Chinese
Timor
Bali
Sandalwood
Java
Batak
Fjord
Northlands
Icelandic Pony
Gotland
Dartmoor
New Forest
Fell
Dales
Exmoor
Shetland
Hackney Pony
Welsh Mt. Pony
Welsh Pony
Welsh Pony of Cob Type
Highland
Riding Pony
Connemara
Camargue
Landais
Merens
French Saddle Pony
Galician and Asturian Pony
Basque
Sorraia
Garrano
Bardigiano
Haflinger
Sardinian
Bosnian
Pindos
Skyros
Peneia
Viatka
Kazakh
Zemaituka
Bashkir Curly
Basuto
Pony of the Americas
Assateague and Chincoteague
Sable Island Pony
Galiceno
Falabella
Australian Pony
Bhutia
Burmese
Sumba and Sumbawa
Nigerian
Syrian

1/2 Breeds & Equine Relatives:
Zebra
Donkey
Mule
Zedonk
Miniature Horse
Miniature Donkey