Chest: Tole's job class is the Fool, and he's a whimsical adventurer with a maxed out luck stat. This results in him doing some amazing things by accident, like instantly mastering the teleport skill and climbing a treacherous waterfall to find Capulet in his treasure chest form. His luck can also be unpredictable in how it hurts or benefits him, since he got separated from his parents when he was young, which led to him mastering the teleport spell and eventually making some unique friends with his kind and caring personality.
Oblivious characters in Death Road to Canada have low wits and a good attitude, and unlock special dialogue options in which they blindly stumble their way into good fortune or out of bad situations. That said, only such characters with high loyalty (another personality stat that is almost always unknown at first) truly fit.
The Jester class in Dragon Quest III (known as the Goof-Off in the NES version) and almost every Dragon Quest game thereafter. They are almost always either uncontrollable or very weak or both in battle, and every stat is a Dump Stat except for Luck, which is where all those points went. Their high luck, however, enables them to have much stronger a chance of inflicting a critical hit when they do successfully attack, and to have a greater chance of a win in the gambling minigames if you can't or don't want to do Save Scumming. Also, in most of the games, after a certain point, they are the only class that can become a Sage (healing AND attack magic) without a special item.
The player can deliberately make their character into this in the Fallout series by giving themselves a high luck stat at the start of the game and can take it even further by sacrificing intelligence in order to do so. A high luck stat will let you pull off feats such as successfully preforming a life saving surgery despite having no medical training, and when combined with a low intelligence randomly guessing a correct password at one point.
Bartz in Final Fantasy V is even introduced to us as a handsome young wanderer going wherever the wind takes him with a trusty animal companion by his side (if a chocobo instead of the archetypical dog). He mostly ends up saving the multiverse because he fell into it, and while he's got an occasionally cynical side it's mostly to say the sort of things the player might be thinking.
Inspector Hildibrand in Final Fantasy XIV adds this to his status as the Cloudcuckoolander: he's genuinely well-intentioned and really wants to help people out, but his staggering... logic... as well as his tendency to rush in where even the Warrior of Light fears to tread, tends to lead to one trainwreck after another, complete with Stuff Blowing Up courtesy of his helpful assistant.
A lot of comic Adventure Game protagonists could fit the bill but Bwana from The Journey Down is exceptional even among them. For proof, he'll fly a seaplane with his eyes closed, install ship (as in, from a yacht) engines on said plane by flinging them with a crane, and attempt to cook with engine oil. And he'll survive and be impressively successful every time.
In Kirby: Squeak Squad, Kirby's motivation for starting his adventure was that his cake was missing. In Super Smash Bros. Brawl, he was revived because, in his hunger, he ate one of Dedede's magic pins.
Johnny Cage, perhaps best demonstrated in Mortal Kombat 9. He was lured to the tournament under the impression that it was a publicity stunt and fights — and defeats — both Reptile and Baraka fully believing them to be guys in makeup. On top of that, he outlives The Chosen One and is one of the game's few survivors.
Willie Trombone from The Neverhood. He's not very intelligent, but he goes behind Klogg's back to help Klaymen and revive Hoborg. He also manages to avoid the fate four of his brothers met in the Hall of Records due to being Too Dumb to Fool.
The main characters of The Prince of TennisDating Sims often fall into this trope and Naïve Everygirl. In Gakuensai no Oujisama, the main kid was a normal second-year girl who happened to be chosen as the one organizing the School Festival with the tennis boys...
In SuperStreet Fighter IV, Ryu is this according to fortune teller Rose, which means he is the only one who can defeat M. Bison for good.
In Street Fighter V, G is associated with The Fool by Rose's student Menat; indeed, he's a mysterious goofball who claims to be "President of the Earth" and posts rambling speeches on Youtube, but ends up winning tons of supporters due to his honesty and charisma.
Reimu Hakurei is an interesting case in that she isn't entirely clueless. However, her mind works very differently from most people's (even considering that "common sense" is a rare thing in the Fantasy Kitchen Sink the games take place in to begin with) and her extreme luck is what allows her to respond to most every incident that occurs with the same course of action: pick a direction at random and go, because no matter what, her luck will lead her to the Big Bad so she can stop them. Amusingly, her best friend is a magician, just like in Tarot.
