You can find penguins in captivity in several aquariums all over the world. However, all known species of penguins live naturally in the southern hemisphere. Contrary to general belief, Penguins do not live only in icy conditions. Outside of Antarctica, Penguins usually inhabit desertic regions and rocky islands where there are not a large number of land predators, so their incapacity to fly is not an issue.
Their habitat ranges from the ice shelf on Antarctica, like the emperor penguin, to some temperate islands near the equator, like the Galapagos penguin. Also, some penguin species live in South Africa and Australia.
The distribution could be viewed like this:
King Penguin
Subarctic islands, Tierra del Fuego, South Georgia Island.
Emperor Penguin
Antarctica.
Adelie Penguin
Ross Sea Region in Antarctica.
Chinstrap Penguin
South Sandwich Islands, Antarctica, South Orkneys, South Shetland, South Georgia Island, Bouvet, Balleny and Peter Islands.
Gentoo Penguin
Falkland, South Georgia, Kerguelen, South Shetland, Heard and Macquarie Islands and the Antarctic Peninsula.
Little Blue Penguin
Southern Australia, New Zealand, Chatham Islands and Tasmania. Some reports in Chile.
Northern Little Penguin
New Zealand, nesting only on Banks Peninsula and Motunau Island.
Magellanic Penguin
Southern cone of South America. Coastal south Argentina and south Chile including the Falkland Islands.
Humboldt Penguin
Coastal Peru and Chile in South America
Galapagos Penguin
Galapagos Islands
African Penguin (Jackass Penguin)
South western coast of Africa.
Yellow Eyed Penguin
New Zealand in the South-east coast of South Island, Foveaux Strait and Stewart Island and Auckland and Campbell Islands.
Waitaha Penguin (Extinct)
Used to live in New Zealand
Fiordland Penguin
Fiorland coast and Stewart Island/Rakiura
Snares Penguin
New Zealand on the Snares Islands.
Southern Rockhopper Penguin
The American Southern Rockhopper Penguin lives in the Falkland Islands and islands off Argentina and southern Chile. The Indopacific Southern Rockhopper Penguin lives in islands of the Indian and western Pacific oceans.
Northern Rockhopper Penguin
Northern Rockhoppers breed on Tristan da Cunha and Gough Island in the south Atlantic Ocean, with the remainder found on St Paul Island and Amsterdam Island in the Indian Ocean.
Royal Penguin
Inhabits waters surrounding Antarctica and breed only on Macquarie Island