When Toyota first crossed the Pacific to enter the America market, its sole vehicles were an underpowered Land Cruiser and a small car that was quickly yanked from the market. The company resolved to Americanize its exports; slowly, they built up a following with the Corona and a small pickup, while still selling a handful of Land Cruisers each year.
As their continuous improvement process went to work, Toyota became known as one of the highest quality automakers in the world. The Corolla, Tercel, and Camry became staples of the America road, and Toyota created new brands for the American market: Lexus and Scion. The Camry, one of America's best sellers, is exported to Japan from the United States, and doesn't sell well there. Even the Corolla gets a new intake manifold for American use - but for a long time, if you wanted an authentic Japanese version, you could get the Geo/Chevrolet Prizm!
Like most automakers, Toyota sells a wider variety of vehicles in Europe and Japan than in the US, including the obligatory diesel and turbocharged models and a range of "minicars." Many vehicles sold in the United States are assembled in North America, including all Corollas and Camrys, and an American runs the North American branch. In short, Toyota is almost as American as Ford, which relies on Asia and Europe for many of its designs.
Enthusiast/history site: toyoland.com