The American Quarter Horse is one of the most versatile breeds,
with affinities for racing, working, and riding. The Quarter Horse
outnumbers every other breed of horse in the world. With a registry
of over a million registered horses he is popular everywhere. The
AQHA has been registering horses since the 1940s which is a
relatively short amount of time compared to the much older Arabian
breed.
It depends on where you are asking about, and for what purpose. Out of stock-breed horses, the most popular is the Quarter Horse. Arabians are popular for a lot of different reasons. Racing = Thoroughbreds, and so on.
The most popular breed in america is the American Quarter horse, followed my The American Paint horse, and other breeds such as the Appaloosa, Morgon, Arabian, and thorughbred.
The most popular breed is the American Quarter horse, just by numbers alone, however most other breeds are just as popular in America. There really is no one 'top horse'.
The top 5, based on numbers, would be the Quarter Horse, American Paint, Arabian, Thoroughbred, Appaloosa. In fact the Quarter Horse is the most popular breed in the world.