3rd planet from the Sun, the Orion-Cygnus Arm, Milky Way Galaxy.
Near Quasar 3C 405.
Earth is a real-life planet on which almost all of Adventure Time takes place. After suffering a major catastrophe brought on by the Great Mushroom War, this planet has lost about a fifth of its original mass, and the crater remains seemingly clean cut, even though about a millennium has passed. Earth is first seen in "The Real You." Only one continent, called Ooo, has been seen so far. The inhabitants of Ooo, mostly speak English, but other languages, such as German and Korean, are shown to still be spoken. Additional areas off of the planet also interact with it, such as the Cloud Kingdom, the Nightosphere, the Crystal Dimension, Lumpy Space, and the Dead World .
While it was always known that Adventure Time takes place in a post-apocalyptic world, the fact that the series is set on Earth was not directly stated until "Holly Jolly Secrets Part II," in which Simon Petrikov (Ice King) mentions that he obtained his crown inScandinavia, a real location on Earth.
In episode "Five Short Graybles," a holographic visual of Earth is seen rotating, much like a desk globe. It is also depicted with a scooped crust, as first seen in "The Real You." In "The Lich" you can see the Earth again, when the Enchiridion opens a map and Jake wish to enhance.
The first known time Earth was actually mentioned by name was in "Sons of Mars," which happened when Magic Man was explaining how the transporter works.
Adventure Time takes place on a post-apocalyptic Earth. This has been hinted at throughout the series. When Jake enhances the view of the universe provided by the Enchiridion, the solar system is shown with a possibly engorged sun and the planet Mercury missing. For a list of references, see: Mushroom War.
The Land of Ooo is the main setting of Adventure Time, and is the home of Finn and Jake, along with all of their friends and foes. It is divided into different kingdoms, but there are also many geographical areas not known to be part of any kingdom. About three other continents can be seen to still exist on Earth.
Technology seems to have gone back a lot, as stated by Jake in "The New Frontier" when he claims that rockets haven't been re-invented yet, but general sciences appears to have gone forward dramatically. Examples of this include creating life, like when Princess Bubblegum created the Earl of Lemongrab, genetic splicing and mutating, like when she was preparing the ingredients for the perfect sandwich, her immortality elixir that she used to bring long dead Candy People back to life, and even in the Adventure Time version of "Frankinweenie", where Marsha brings Dusk back to life.
Another example of this is building inventions, like when Marsha reveals her invention of a time machine.
Due to the Great Mushroom War, magic runs rampant across Earth, or at least just in Ooo. Merging magic with science seems to happen a lot though, and the two may go interchangeably with scientists, but not with spell-casters. However there is some evidence of magic existing previous to the war as evidenced by Ice King's crown magically changing him and the environment around him before the war started.