It's not easy find information about ALL horse breeds in the world, let alone a good photo. But I'll try my best.
South and Middle America
USA & Canada
Central, southern and eastern Europe
Russia and neighbours
Suffolk mare Chickering Marion 2nd. Although this mare is born in 1954, it resembles a great example of Suffolk breed even today. Sturdy, punch-like body, overall powerful conformation, short legs with only little feathering and chesnut color. Yes, chesnut, for some reason the color of Suffolks is written this way. As probably all drafts, Suffolks are quite rare today.
Lokai comes from the mountain region of Tajikistan. It's usually small, pony-sized but nevertheless hardy, strong and surefooted. It's used by local tribes as a riding and pack horse, sometimes also as a light draft. It's also used for racing and for local horse game Kokpar. Its ancestors are the Lokai tribe's native horses that have been improved with Central Asian, other Russian and European horses.
Umour by Gypsy Cob, via Flickr. Ardenner Horse is one of the oldest breeds, it's suppsed to live in Ardennie area more than 2000 years ago. They've been powerful drafts with good quality and Ardenners have been used for breeding other heavy breeds. Now it has 2 types, lighter Postier and heavier Ardennes du Nord. Sometimes also Auxois is considered to be a type of Ardenner, not a breed of its own. Ardenners are usually bay or gray, but they can be also chestnuts. Black is not accepted.
Rhinelander gelding Lord De Luxe. Rhinelander is closely related to Westfalen, they both come from Warendorf stud. Rhenish Horse Studbook was founded in 1892. Lately lots of TB's, Trakehners and other German WB's have been used for breeding Rhinelanders. Rhinelander is like any other German WB: long-lined, noble, has elastic gaits and good rideability. All in all, it's a suitable breed for competing in the highest levels of show-jumping and dressage.
Catria horse (cavallo del catria), © Gianni Marcelli. Catria horse comes from the mountainous area of Catria, middle Italy. Its ancestors are mainly Maremmanos and is supposed to be a very old breed, too, at least 1000 years. They were used as mounts for both soldiers and civilians but both World Wars diminished its numbers dramatically. The breed is still extremely rare. They're not high, usually 147-150 cm at withers. common colors are black, bay, gray, and roan.
Kiger Mustang mare. Kiger is a substrain of Mustang. They were found in Oregon. Kigers are homogenous with similar color and conformation and they have been DNA-tested for close relation to the Spanish horses. They're usually dun or grulla with dun markings (zebra stripes, dorsal stripe etc) and their conformation resembles still their Spanish ancestors: compact, quite muscled, somewhat noble and smooth. They also have a tractable temperament.
Estonian Native gelding Eksel. Estonian Native is an old breed, there has been horses in the area of modern Estonia about 3000 years. They were bred by local farmers but during the Soviet time the breed almost disappeared as it was not used for agriculture. Estonian is quite small, height at withers is usually 138-148 cm. It comes in all solid colors.
Westphalian gelding Rio De Janeiro. Westphalian or Westfalen comes from Germany, Warendorf stud. The stud was founded in 1826 but even before that year there had been horses with good quality in Westphalian region. The studbook was opened in 1888. The modern Westfalen is a well-moving warmlood with good rideability. The most famous Westfalens are probably Ahlerich and Rembrandt, both won Olympic medals in dressage. They're usually black, bay, gray, or chestnut, other colors are very rare.
Moriesian mare Aurora LaBella Luna. Moriesian is a cross between Morgan and Friesian, ideally combining the best features of both breeds, being showy and somewhat regal but also versatile and calm. Morgan percentage must be 25-75%. Usually they are blacks or bays but all colors are acceptable and via Morgan there may be palominos and buckskins, duns, grays, silver dapples etc.
The Treehugger website claims this is the only photo of a living Tarpan. Tarpan, or Eurasian Wild Horse, lived on the steppes and forests of east Europe, Poland and Russia. They were hunted and captured (then crossed to domestic horses) until late 19th century when they were extinct in the wild. Later the captured pure individuals also died and Tarpan became extinct.
Kiso Horse comes from what is now known as Nagano Prefecture, central Honshu. It's an ancient breed, mentioned first time in 6th century. Its name comes from Kiso River. Its ancestry is unknown. During the Meiji period Kisos were crossed with imported horses but some escaped this and purebred Kisos still exist today. They're very rare, though. Usually they're bays, chestnuts or grays and height is about 135 cm.
Silverthorn Shotgun, Australian Stock Horse stallion. ASH seems to have a similar history as Waler: developed from the imported horses and being suitable to Australian sometimes harsh conditions. Waler doesn't have Quarter Horse blood, ASH does (well, not all). As the name goes, ASH's have been used as stock horses and they're known for their intelligence, stamina, courage and toughness. Today they're used in many disciplines: dressage, endurance, polo, eventing, cattle work...
Kaimanawa horses, © Jan Maree Vodanovich. Kaimanawa wild horses live on the Northern Island of New Zealand. The first horses were brought to New Zealand in 1814. Kaimanawas have some Exmoor, Welsh and Arabian blood in their veins. Once a year, Kaimanawas get mustered and counted and, as for the number of horses must kept sufficiently low to avoid habitat destruction, some horses are separated from the herd. Some find a new home, some end up at the slaughter.
Belmont Golden Boy, a New Zealand Warmblood (NZWB) stallion. NZWB is simply a warmblood riding horse that is accepted by New Zealand Warmblood Horse Breeders Association. Most of the NZWB's have TB, Anglo-Arab, Trakehner, Hanoverian, Oldenburg or Holstein background but also other European WB's are accepted. The breeding goal is to produce good dressage horses and jumpers.
VBA Belle, a captured Brumby mare. Brumbies are the semi-feral horses of Australia. Similar story as the Mustangs': horses were imported to Australia and then either let free or they escaped. They are considered harmful to the native vegetation, soil and animals and also to the domestic animals, and thus they're hunted and captured. Brumby conformation is varied as are the colors. They're very tough and surefooted horses.
Coffin Bay pony is a semi-feral pony of Coffin Bay, on the southern tip of the Eyre Peninsula in Australia. It's not a Brumby, Coffin Bays and Brumbies are kept separated with fences. CBP originates from 60 or so Timor ponies that were imported to Coffin Bay area in 19th century. Also some European blood has been mixed to the ponies. They still look a lot like Timor ponies but there are 2 types of CBP's, light saddle type and a stronger type.
Haydon Legacy, an Australian Waler stallion. Walers' ancestors are all the horses that were imported to Australia so it was a very diverse stock. There were TB's, Arabians, Timor Ponies, drafts, some Southern African horses and so on, but not QH's. On 19th century, Walers were cavalry mounts par excellence, they were imported to Palestine and India. Nowadays some sources claim that the original Waler has merged into the Australian Stock Horse but some claim there still are some bloodlines left.
Koora-Lyn Cossack, 5th generation Australian Pony stallion. Australian Pony's history started in 19th century and the studbook was formed in 1931. Australian Pony's ancestors have been Arabian's, TB's, Welsh and Timor Ponies and several other horses and ponies imported to Australia. Even today crossings with Welsh A and B are permitted so Welsh blood is dominant and it's also seen in the conformation of AP. They're pretty, beautiful ponies with lots of capacity as riding and driving ponies.
Riwoche Horse/Pony was found in an isolated valley in Riwoqê County, Tibet in 1995 but, of course, the locals have known them forever. The horses are wild or semi-wild, some are captured for work but often released again. They are very tough and look primitive, resembling somewhat the Przewalski horse. They've lived isolated for a long time without any foreign influence. They're pony-sized (122 cm), always dun colored.
Sumba and Sumbawa ponies are closely related to each other and bred in neighboring islands of Sumba and Sumbawa, Indonesia. They're fairly primitive, their ancestry is not known but they have lived on their home islands for a long time. They're traditionally used for native dancing and lance-throwing competitions but also as riding and pack ponies. They're small, usually not more than 120 cm at withers and dun is claimed to be the most common of colors.
Kuda Padi pony is a local Malaysian pony breed. Its ancestry is not known, suppose the ponies were once imported from China, Vietnam etc. They're very well adapted to the tropical environment: they can utilize the local grasses without any artifical forages and are resistant to parasites. They're pony-sized, some 140-145 cm at withers and usually bays with occasional white markings.
Manipuri Pony comes from Manipur, India. It's an old breed, thousands of years old even if its ancestry is not very well-known. Probably their ancestors are the Mongolian and Tibetan ponies but also some Arabian crossings have been made. Manipuris are the original polo ponies. Manipur is quite small, some 110-132 cm at withers and it's fairly lightly-built, even elegant. Usually they're bays and chestnuts, but also other colors, such as tobiano, gray, and perhaps palomino, may occur.
Yonaguni Horse/Pony originated from Ruykuy Islands, mainly Yonaguni Island, located south-west from Japan main islands. It's an old breed and its ancestors are unknown. Though, it resembles Tokara and Miyako Ponies a lot. It's also very rare, they were used for transportation and as drafts but mechanization made them useless. They're usually some 110-120 cm at withers but strong compared to their size. Yonaguni hasn't been crossed with bigger horses so it's kept its native features.
Misaki uma (御崎馬/岬馬) or Misaki horse/pony is from the 18th century, the first historical records of the breed are from 1697 but it might be older. They're from Miyazaki prefecture, Kyushu, so sometimes they're called Miyazakis. They live as feral horses. They suffered a lot during the WWII and the numbers were declined heavily. Nowadays there are few hundred Misakis left and the breed is maintained. They're small animals but despite the small size they look more like horses than ponies.
Indian half-bred (IHB) mare Hirni. IHB was created by Indian army during 19th century as good cavalry horses were needed. It was created by crossing TB's and Australian Walers with local oriental horses, Kathiawaris and Marwaris. The result is a horse suitable for Indian climate and a good riding horse. Nowadays the Indian Riding Police uses IHB's. They're usually some 150-160 cm, type varies, some have distinct TB features, some have the curved ears of Marwaris. All colors are accepted.