Because penguins are an endangered species, the U.S. (and many other countries) have strict laws regarding importation, sale and ownership. It's generally prohibited for private parties to own penguins.
There are certain places in the world where penguin ownership is permitted, but specific permits or licenses are required. Even with these permits and licenses, only four types of penguins may be kept as pets. These are fairy penguins, wingless fairy penguins, emperor penguins and African penguins.
Fairy penguins are typically about 34 centimeters in height, weigh approximately 3 pounds and are a bluish color. They enjoy swimming most of the day. Wingless fairy penguins are similar to fairy penguins except their flippers have been cut, so they prefer to spend their time on land. Emperor penguins are larger at about 125 centimeters in height and weigh between 22 and 45 kg. They only live in extremely cold environments. African penguins are tall (about 3.3 meters) penguins that prefer to live under rocks. They are the rarest and most expensive breed.
An alternative to penguin ownership is adoption. Many zoos and charities, such as the World Wildlife Fund, offer programs that allow penguin enthusiasts to symbolically "adopt" a penguin in exchange for a donation.