Mushroom War

The Great Mushroom War is the cause of the post-apocalyptic setting of the Land of Ooo. Not much is known about the war at the moment, but the inclusion of "Mushroom" in the title is probably referring to a mushroom cloud generated from a nuclear bomb. If so, then it is likely that the Land of Ooo and the creatures who inhabit it were created from the nuclear fallout that irradiated the land. This is further supported by the ruined pieces of modern technology scattered across the land, and the beginning of the opening theme (which briefly shows the remains of nuclear bombs and other weapons). It was confirmed by Pendleton Ward that Marceline is a survivor of the war due to her supernatural powers.

The first mention of the war in continuity was in "Video Makers," when Finn and Jake discover government warnings before the movies they watch for their film club. Even though the civilizations that created these warnings would have been long gone by their time (and that films bought for home video usage generally are protected to be used for private usage only, which being held in a home would be considered as such), they decide to abide by them to prevent from breaking the law.

Strangely, the Land of Ooo also contains technological devices that are far more advanced than what exists today, such as Universal Translators and Holographic Newspapers. It's unknown whether these are based on pre-war technology or are more recent inventions.

Evidence or clues of former civilization
In many episodes of Adventure Time, there are many hints or clues regarding the world and the civilization that existed prior to the Mushroom War, including as follows:
 * Adventure Time Theme Song: An opening shot showing various debris of destruction, including grayed land and undetonated nuclear missiles lying around, as well as a decaying arm in a tree trunk.
 * Tree Trunks: Traffic signs, which have since somehow mutated into Sign Zombies. It is unknown how this has happened.
 * Business Time: Ancient artifacts frozen in icebergs, including baby shoes and the Businessmen. Finn also uses a flamethrower built from two fuel tanks connected to a rifle by a tube.
 * The Witch's Garden: The remains of a highway system and a plane's wing can be seen near Gary's nest; the River of Junk is essentially a river of mundane pre-war artifacts.
 * Ocean of Fear: Underwater city ruins and vehicles appear, and a brief scene shows a damaged aircraft carrier and a stranded tank- an even briefer scene depicts two dead bodies on a couch in the remains of a pre-war living room. Finn and Jake also take to the depths in a submarine. You can also see the remaining tops of cars while theyOcean_of_fear,_dead_people.png are floating over what might have been a ancient road.
 * City of Thieves (episode): When Finn and Jake are in Penny's tent, a double barrel shotgun can be seen sitting among a pile of gold coins.
 * Storytelling: There are many remains of radios and debris scattered throughout a forest.
 * The Other Tarts: Various boats and whale skeletons can be seen in the Desert of Doom, suggesting that it may have previously been a body of water.
 * The Silent King: The storyboard for "The Silent King" contains the first time The Mushroom War is mentioned by name in the series, heard when Gummy is reading from the rule book. "In response to elder Gorflox's repeated requests for an organized response to bike thefts caused by the caotic fallout from the great Mushroom War an exploratory rules committee was hastly established by executive order... (trailing off)" However, this line was cut from the actual episode.
 * The Real You: A shot of Earth appears, and a huge chunk of it is missing.
 * Death in Bloom: Debris of civilization, including numerous police vehicles, in the Land of the Dead.
 * Susan Strong: The Hyoomen Tribe live in the ruins of an underground city. In the storyboard, a warning reading "Biohazard Danger" appears on the hatch, although this was cut from the episode. The inhabitants were possibly humans driven there during the war and later mutated.
 * Go With Me: The Drive-In Theater houses the remains of many cars.
 * Belly of the Beast: The remains of a car rest in the throat of the monster as Finn and Jake return to confront the bears in the stomach.
 * Video Makers: Video cassettes feature movies such as Heat Signature that were made prior to the war. Jake even mentions the Mushroom War in the episode.
 * Mortal Folly: The base of The Lich's power is an abandoned, ruined subway station with deserted trains and littered with human skeletons scattered on the floor as if they had been killed that very moment around the station. Character designer Andy Ristaino has stated that these skeletons "were supposed to feel like they were east coast commuters ... all bundled up for winter." Outside the station is what appears to be a nuclear missile. There are also ruins of buildings in the backround
 * Mortal Recoil: While it is unknown where they would get them, Jake implies that the Lich's "Well of Power", which he recreated in Princess Bubblegum's bathtub with various chemicals collected by Finn, is a vat of toxic waste left behind in his former lair.
 * Heat Signature: In front of Marceline's Cave there is a torn up highway that acts like an awning. There is also the remains of an old car across from the cave entrance. Later, the ghosts take Finn and Jake to the top of what looks like a torn up skyscraper with a helicopter crashed on the roof.
 * Memory of a Memory: Many of Marceline's childhood memories appear to be around the ruined remains of civilization: she is seen as a little girl living in a ruined city with a derelict tank near her home, then later catches her father eating her fries at a destroyed diner. This could be the fallout of the Mushroom War, which could cause a continuity problem, or it could be wreckage from a previous military conflict that eventually escalated into the Mushroom War.
 * Hitman: Outside the Breakfast Kingdom is a desert with an abandoned train in it, also a sewer pipe leaks out water for the moat around the castle.
 * The Monster: When Finn and Jake find the villagers various metal tools are on the ground.
 * Wizard Battle: The arena for the battle seems to be an abandoned football stadium.
 * Legends of Ooo, a game on cartoonnetwork.com, mentions the Mushroom War. If you click on the radio in Marceline's house, Jake states that, "They stopped making these before the great Mushroom War."
 * The Creeps: A portrait of what appears to be of New York City's silhouette.

Timeline
It is unknown just when the Mushroom War took place. In the episode "Her Parents" it is stated that the Rainicorn-Dog Wars took place over "thousands of years." However, this does not prove when the Great Mushroom War happened, since the Mushroom War went on in the land that is now Ooo, but the Rainicorn-Dog Wars took place in the Crystal Dimension. Or alternatively Jake may have exaggerated for drama's sake and simply meant "a very long time" when he said that.

In "Memory of a Memory," Marceline appears as a young girl in a post-apocalyptic environment. In this scene, a burning city in the background suggests the Mushroom War occurred fairly recently, although plants growing in the wreckage of a house could suggest some time has passed since the calamity happened, but it has also been noted in nuclear testing and usage (e.g., Hiroshima) that the radiation encourages plant growth and days after nuclear bomb droppage occurs plants and flowers start to grow like weeds. Because Marceline has been confirmed to be approximately 1000 years old, this could mean that the Mushroom War took place just under 1000 years before the events of the series.

It could have happened sometime in the future considering the advances in technology.