Abraham Lincoln debuts in the original animated short, where he encourages Finn to believe in himself after warping his brain in the past and to Mars. He is also seen in "Business Time," where he is a character included in a game on BMO.
He is referenced in "Crystals Have Power." Jake states, "If I had a penny for every time someone went crazy hopped up on magic energy... I'd be Abraham Lincoln!"
He is referenced in Issue 3 of the Adventure Time comic. When Finn is telling everyone how to beat The Lich, he says that just like Abraham Lincoln said in the past and on Mars, "you need to believe in yourself."
The first time he ever appeared in the official series is in one of the many pictures in Hunson Abadeer's house. He is a major character in the episode "Sons of Mars," and is the King of Mars. He lost his immortality (and seemingly his life) in the episode in order to save Jake after he was accidentally killed and sent to the 37th Dead World. As a result, he turned to stone, and became a statue for all of eternity.
Abraham Lincoln is modeled closely after the real-life Abraham Lincoln. He wears a black suit with a black bow tie. Two major differences from his real-life appearance are that, in the show, he floats like Marceline, and he has a yellow light surrounding his head (at least in the animated short). He also doesn't wear his famed stovepipe hat. Unlike most characters, his hands have five fingers. He sits atop a throne that is engraved with the symbol ♂, the astrological symbol of Mars, which has come to also represent "male" in contemporary popular culture. This symbol can also be found in the arena in which Abe Lincoln sits.
Lincoln speaks in a colloquial vernacular of the late 20th Century, much different from his published speeches in the 19th Century. He uses phrases such as "bums me out" and "I remember when you were really cool" and is extremely expressive and emotional, especially during his sentencing of Magic Man. He is not without subtlety, however, such as the private joke he shared with Death.