Throughout the Earth's known history, there have over a dozen continents and continental configurations that no longer exist today. On the broadest level, they tend to follow the "supercontinent cycle" -- continents combine together to form one giant supercontinent, then break again into separate continents, then the process repeats again. A full cycle occurs about once every 300-500 million years. The last supercontinent was Pangaea, which existed about 200 million years ago, and before that, Rodinia, which existed about 700 million years ago.
Some of the most famous continental configurations that no longer exist today are Pangaea (which contained the world's entire land mass except for a small part of present-day China), Gondwana (South America, Africa, Australia, and Antarctica all merged together), Laurasia (North America and Eurasia together), Baltica (a small subcontinent made up of the present-day Baltic states), India (once an independent subcontinent), and the Kerguelen continent (a continent in the southern Indian Ocean that sunk underwater 20 million years ago).
The most well-known of all the ancient continents is Pangaea. Forming about 250 million years ago, right after the Earth's worst mass extinction ever, Pangaea persisted for about 70 million years, until it broke into three pieces -- Laurasia, Gondwana, and Africa -- about 180 million years ago. Pangaea was a C-shaped landmass straddling the equator that consisted of more than 98% of the present-day total continental area. Pangaea was so huge that it would have been possible for animals to walk from the South Pole to the North Pole via land alone. This was the only known time in which such a thing was possible. A continuous north-south landmass also encouraged oceanic mixing which meant the temperature was relatively warm and uniform over the entire surface of the Earth.
The dinosaurs initially evolved on Pangaea. The early dinosaur faunas were global in extent and all ate the same food: cycads, conifers, and each other. Then, as Pangaea began to rift apart 180 million years ago, dinosaurs began to strongly differentiate on the basis of their native continent. Three groups split from each other based on the three major continents at the time. About 130 million years ago, South America began to drift apart from Africa, leading to the creation of a full-fledged Atlantic Ocean by 110 million years ago. About 60 million years ago, just after the dinosaurs went extinct, North America began to split from Eurasia, creating the Norwegian Sea.
The remaining continents -- Laurasia, South America/Antarctica, Africa, Australia, became the home of the new dominant creatures on Earth, the mammals. Even as early as 90 million years ago, the first members of the mammalian clade Laurasiatheria (hoofed animals, moles, shrews, bats, carnivorans, hedgehogs, cetaceans, and many more) and Euarchontoglires (rodents, lagomorphs, treeshrews, and primates) evolved on the continent of Laurasia. Meanwhile, superorder Afrotheria (golden moles, elephant shrews, tenrecs, aardvarks, hyraxes, elephants, manatees, and others) evolved on the island continent of Africa. Australia and South America were dominated by marsupials. Eventually, Laurasia split, dividing those groups into two, and Africa collided with Eurasia, exchanging fauna between the two. Just three million years ago, North America touched South America at Panama, and the most recent faunal interchange occurred, mainly to the detriment of the South American animals.