A list of cars manufactured in Japan is available online at ListofJapaneseCars.com. This website lists the majority of Japanese car brands and provides a link to a list of the models available.
Wikipedia also provides a list of Japanese car makes and models. This list contains defunct as well as current makes, as of 2015.
The first cars made in Japan were simply copies of American and European vehicles. Uchiyama manufactured the first car in Japan in 1907. Japan truly started contributing to the motor vehicle industry after World War II. After Ford, General Motors and Chrysler opened plants in Japan, the government enacted laws to give the domestic car industry more leverage.