There is a great deal of controversy over the actual role of the heavy horse in ancient times, particularly the Middle Ages. Some believe that they were developed as war horses, large enough to carry the weight of their own armor as well as an armed and armored rider. The "Great Horse," as this giant was called in England, was a descendant of the so-called Equus robustus, the largest of the original types and native to Europe. (The existence of such a type of horse would not pre-suppose macro-evolution.) The Flemish horse was bred from this ancient type, and it became the basis for later draft breeds; its modern equivalent is the Belgian horse. The Belgian, in turn, was used by the French to breed their Norman horse and most draft breeds developed from this foundation. (It is also noteworthy that not all scholars subscribe to the belief that the "Great Horse" was really so great...it is quite possible, the medieval knights being small men, that they were no bigger than the Friesian or Andalusian of today.)
Heavy horses also pulled the heavy, unsprung carriages of medieval times over the rough roads of Europe and Britain, and eventually they supplanted oxen for farm use. After gunpowder revolutionized warfare in the 17th century, they carried on in peaceful tasks. In the United States they supplied power for the tremendous agricultural expansion of the 19th century.
Mechanization in the 20th century largely deprived the heavy horses of their usefulness, and their numbers have declined greatly. They still work on many farms, however, and they may be seen today at state fairs, in events such as breed judging and weight-pulling contests. The continuance of these breeds seems assured, thanks to horsemen who value their ancient lineage and heroic proportions.

Ardennes

Auxois

Belgian

Boulonnais

Breton

Clydesdale

Comtois

Dutch Draft

Finnish Draft

Gypsy Vanner

Irish Draft

Jutland

Latvian

Lithuanian

Noriker

Percheron

Poitevin

Russian

Schleswig

Schwarzwald

Shire

South German

Suffolk Punch

Trait du Nord

Vladimir

Feral

Brumby

In addition to the fact that the Albino as a breed is generally called the American Albino, it is also noteworthy that there has also been mention in the past of the American Buckskin and the American Cream.  The Paint and Pinto have also been titled American in the past.  Among the "Anglo-" horses also there are those with which we are less familiar--for example, the Anglo-Argentine, a South American cross between the native Criollo and the Thoroughbred, which is popular as a polo pony.
Before the era of the automobile, several breeds of the so-called Coach horse were developed for drawing vehicles of various types.  In an average of five stallions, two geldings, and one mare, listed as "Coach" horses and exhibited at the Columbian Exposition at Chicago in 1893, the height was 63 7/8 inches (62-66) and weight 1274 pounds (1175-1375).  Accordingly, these horses were very similar in size to the present-day German breed known as the Hanoverian.  Presumably the Coach horses at the Columbian Exposition included importations of both the French Coach and the German Coach breeds.

Akhal-Teke

Albino

Alter-Real

American Saddle Horse

Andalusian

Anglo-Arab

Anglo-Kabarda

Anglo-Norman

Appaloosa

Arabian

Australian Stock Horse

Avelignese

Azteca

Barb

Bashkir

Budyonny

Camargue

Canadian Cutting Horse

Carthusian

Cleveland Bay

Criollo

Danubian

Darashouli

Deliboz

Døle

Don

Dutch Warmblood

East Bulgarian

East Friesian

East Prussian

Finnish

Finnish Universal

Frederiksborg

Friesian

Furioso

Gelderlander

Gidran

Groningen

Gypsy Vanner

Hackney

Hanoverian

Hispano

Holstein

Iomud

Jaf

Kabarda

Karabair

Karabakh

Kathiawari

Kiso

Kladruber

Knabstrup

Kustanair

Lipizzaner

Lokai

Lusitano

Masuren

Mecklenburg

Missouri Fox Trotter

Morgan

Mustang

Nonius

Oldenburger

Orlov Trotter

Palomino

Paso Fino

Persian Arab

Pfalz-Zweibrücker

Pinto

Pleven

Polish Arab

Pomeranian

Quarter Horse

Rocky Mountain Horse

Rottaler

Shagya Arab

Standardbred

Tchenarani

Tennessee Walking Horse

Thoroughbred

Turkoman

Trakehner

Waler

Westphalian

Wielkopolski

Württemberg

Ponies are small horses that come in a great variety of sizes, conformations, and personalities.  Some pony strains trace back to antiquity, while others are even now being developed by breeders.  Though their size (14.2 hands and under) makes them suitable for children, they should never be pampered as pets.  A pony thrives on a hardy life and--if possible--the company of its own kind.
Some show ponies are fine examples of pure native breeds, but most are part Arab or Thoroughbred.  Although showing classes are for different sized ponies (suitable for children of a specified age group), show conditioning and breeding often make these beautiful little animals beyond the capabilities of the average child rider.
The smallest recorded horse was a stallion called Little Pumpkin; foaled on April 15, 1973; he stood 14 inches high and weighed just 20 pounds in 1975.
The Balearic or Majorca pony is an ancient breed found on the island of Majorca.  A peculiarity of the breed is that in galloping it carries its head (lower jaw) in close contact with its neck (rather than stretched out forward as in Algerian and Andalusian horses).  For this and other reasons it is believed by some that these ponies may be descendants of the Greek horse of Classic times, which was usually portrayed with its head and neck in the flexed attitude described.
The Batak or Deli pony is a small, Arab-derived pony bred in the Batak hills of Sumatra.  The color is generally brown, although skewbald specimens occur, and it stands around 44-50 inches tall.  The Burmese or Shan pony is bred mainly by the hill-tribes of the Burmese Shan States.  It is similar to, and possibly a relation of, the Mongolian pony, and is characterized by great strength for its size, and a rugged constitution.
The Huzulen is a mountain pony native to Rumania, but used also in Poland and perhaps other European countries.  It stands 53-57 inches tall and is black, dark brown, or dark bay, sometimes with white markings on the head and feet.  Like many another pony breed, the Huzulen has Arab blood in its makeup.
The Timor pony is a sturdy breed of pony used in Australia and New Zealand both for riding (particularly stock work) and in harness.  The Timor comes in virtually all colors, including an Appaloosa type having a dark ground color with light spots and a light mane and tail.  Although small in size, the Timor pony is capable of carrying a heavy rider for hours on end without tiring.
The Veglia is the native pony of the island of Veglia (Austria) in the Adriatic sea.  It stands 46-52 inches tall.  Supposedly the Veglia is similar to the Icelandic pony and is probably descended from the South Russian tarpan.

American Miniature Horse

Australian Pony

Basuto Pony

Bhutia Pony

Bosnian Pony

Caspian

Cayuse Indian Pony

Cheju

Chincoteague Pony

Chinese Pony

Connemara

Dales Pony

Dartmoor Pony

Dülmen

Exmoor Pony

Falabella Miniature Horse

Fell Pony

Fjord

Galiceno

Gotland

Hackney Pony

Haflinger

Highland

Huçul

Icelandic

Kazakh

Kentucky Saddle Pony

Konik

Lundy

Minho

Misaki

Miyako

Mongolian

New Forest

Noma

Nordland

Pony of the Americas

Sable Island

Sardinian

Shetland

Skyros

Spiti

Sumba

Taishuh

Tokara

Viatka

Welsh Cob

Welsh Mountain Pony

Welsh Pony

Welsh Pony of Cob Type

Yonaguni

Cob:  A name applied to various types (not breeds) of riding horses of sturdy build, generally described as being short-legged and of large girth.  The Welsh Cob, however, is a definite breed, of two types, used for riding and for draft, respectively.
Hack:  A British term used in reference to a refined riding horse.  To be differentiated from Hackney, which refers to a harness horse originally known as the Norfolk trotter.
Liberty horse:  Not a breed, but any of various types of horses, usually all of the same color, used in the circus to perform singly or in groups while unridden and undriven and controlled only by a ringmaster on foot.

Hunter

Polo Pony

Donkey

Przewalski

Tarpan

Wild Ass