There were numerous small automobile manufacturers in the US in the early part of the 20th century before WWI. Most of these manufacturers were long gone by the time of WWII, but there are a few that were around in the post WWII years.
One of the best known is Tucker. Preston Tucker manufactured the 1948 Tucker Sedan in 1948. He put together his own car company and was only able to produce less than 60 prototype vehicles. There was a very public financial scandal that the press followed which ultimately lead to the dissolution of the company. It is commonly believed that the "big 3" auto makers in Detroit were behind generating the public controversy to eliminate a new potential rival. There was a Hollywood movie produced in 1988 about this called Tucker: The Man and His Dream. It was made by George Lucas and Francis Ford Coppola, both of whom own one of the original Tucker automobiles.
Another auto manufacturer that went out of business is Glasspar. Founded by Bill Tritt in 1949, the company started as a fiberglass boat building business that started branching into cars. They made the G2, a spots car with an entirely fiberglass body. The car was produced for about 3 years, when the board of directors decided to abandon the car company and focus on the boat business instead.