I could see fighter, too; maybe he uses power attack a LOT. Maybe leap attack, too. Thing is, in my head, the little guy's got some serious levels. He's gone toe-to-toe withSpoiler1000 year old vampires, said vampires Eldritch Abomination dad, the Lub-Glubs, the Lich King... even the Ice King is pretty powerful, despite his crippling handicaps.
Assuming, for a second, that that's true and the dude's got two-digit levels on him, does he really show off the range of feats a fighter of that level would have? I suggested Paladin of Freedom because he sometimes lays down some vicious smacks that could be Smite Evil, but he definitely isn't lawful enough to be a vanilla Paladin. Also,But alternately, I can't help but thinking off the look on his face sometimes. Guy's definitely got some valid anger issues- could it be barbarian rage? My initial thought was he's probably about level 17 for the barbarian Tireless Rage feature. The only time I remember him being seriously tired after flipping out and winning was versusSpoilerthe Fight King episode illustrated the little dude's got a pretty awesome will save!SpoilerMarceline's Dad.
Your 1st edition theory carries some water, too, for sure! Maybe 'the Human' isn't just a title. :P
I think there's a 3.5 template for gelatinous creatures; that could fit Jake, I guess, but I'm pretty attached to my idea that Jake is some dude's totally awesome wizard character, transplanted to play with Finn and trying not to wreck the fun for him.
EDIT: The Trap Sense ability fits Finn pretty well, too, actually; after all, HE'S IN HIS ELEMENT!!!!!!