Probably the most common example of a government-owned corporation is the United States Postal Service. Other examples include the National Fish and Wildlife Foundation, the National Park Foundation, the Export-Import Bank of the United States, the Peace Corps and Amtrak.
Freddie Mac and Fannie Mae are considered government owned, though they're referred to as "government-sponsored enterprises," a term given to many financial service corporations under U.S. ownership. Natural monopolies, such as those dealing with energy, infrastructure and natural resources are often connected to a government-owned corporations. The companies vary from total ownership by the government to having stockholders, in which case the state is a majority owner.