Ron Stoppable from Kim Possible has elements of this, notably the "blundering towards success" part. As he puts it, upon being called on his blundering: "Not dumb luck, Kim! Dumb skill!"
Just call it The Ron Factor!
Meatwad from Aqua Teen Hunger Force occasionally fits the description. Even when "bad" things happen to him, karma pays him back almost immediately. (i.e. Shake sells him to the circus and he becomes the star attraction, Shake sticks him in the dryer and he gains super powers. etc.)
Subverted in Codename: Kids Next Door, "OP TRIP." Two Evil Minions stalk ditzy Numbuh Three on her trip to Tokyo. Numbuh Three is too clueless to notice she's been followed, but she manages, purely by accident, to get the stalkers attacked by a mean dog, thrown in a dumpster, catapulted out of a moving train, etc. The minions give up in agony. Then they discover that the dog, the dumpster driver, the train driver, etc. were all Numbuh Three's not-so-ditzy allies in disguise.
Mikey Simon from Kappa Mikey is this trope in a highly concentrated form.
This is lampshaded a few times In-Universe, as the main reason he does get away with some of the crap he causes is because he's the star of a hit TV series.
A bizarre example of the trope, the band Dethklok in Metalocalypse are evil, in an apathetic kind of way. They aren't that intelligent (except in contracts) and accidentally cause death and destruction everywhere they go. Yet they're oddly immune. Oh, they'll accidentally set off explosions and laser beams and falling debris that kills off everyone around them, especially people trying to kill them; but it will miss them every time. And they won't even notice; not that they would care.
Homer Simpson. In the episode "Homer Defined," Homer's accidental prevention of a meltdown at the nuclear plant inspires the phrase "to pull a Homer," meaning "to succeed despite idiocy."
The Infamous "Homer's Enemy" episode deconstructs the living hell out of this trope by showing how a "normal" person would react when having to work with a person who constantly succeeded at life when they by all rights shouldn't.
Inspector Gadget is definitely a poster boy for this trope, in particular whenever assassins are targeting his life directly. While some of his success (and survival) comes from Brain and Penny's heroic efforts, just as many of Gadget's oblivious victories spring from his endless fountain of slapsticky luck (ex. he calls for a certain gadget, but the wrong one comes out which then nails the bad guy—even funnier, the clueless inspector then apologizes for the mishap).
Most of the "Golden Age" Warner Bros. cartoons (Bugs Bunny et al.) embody this trope at some point. Generally speaking, the more "innocent" the character, the better it works.
Cal of Undergrads, who has more friends and more sex without trying than any of his friends combined when they do. At the same time though he has a huge Hate Dom mostly from guys who he has stolen girlfriends from, who have actually started a website against him.
Gimpy: It appears to be stories from people who have come into contact with you. And hated it.
Gimpy: Cal, this website is not a good thing! People hate you! A lot!
Bradley is Stickin' Around's signature fool, mainly due to his interests and general personality. How he is Stacy's Black Best Friend is beyond anyone's interpretation.
Russell is merely the secondary one, since he's just flat out clueless.
Rocky and Bullwinkle: Bullwinkle J. Moose is portrayed as a fool despite him starring in segments that intend to teach. In fact, when Boris used a gas to turn the whole world (including Bullwinkle's friend Rocky) into morons, Bullwinkle is the only one unaffected because he already is a moron.
Pinkie Pie is pretty much the comic relief: quirky, airheaded, and totally laid back about life. Put her in front of all but the most obvious danger and she'll dance around without a care, and it's been hinted that, despite her natural baking skills, her mental instability makes her laughably bad at her job. On numerous occasions, however, Pinkie has calmly and efficiently danced right to the heart of whatever problem has occurred, sped personal development in others, or demonstrated obscure knowledge that even the resident Smart Pony didn't know. After her brilliant solution to the parasprite problem, she stated that even she doesn’t really understand herself sometimes. Even then her methods are so bizarre they're self-defeating; for example the parasprites would have been stopped almost immediately if she had just told people what she knew instead of spending the whole episode hunting various instruments.
There's also Derpy Hooves, a wall-eyed background pony whose made out to be a clumsy, airheaded goof. Then she shows up at the Royal Wedding, attends the exclusive Grand Galloping Gala (in the VIP zone, no less), and is shown amongst an image of the Canterlot Elite. Airhead or not, she's clearly loaded or has some serious connections with nobility.
Charlotte in Making Fiends. Cheerfully oblivious to the fact that her "friend" Vendetta is trying to kill her with an army of toothy, vicious monsters who have the entire town they live in terrified into submission, she usually ends up befriending the fiends as well, and even keeps one as a pet.
Aang from Avatar: The Last Airbender. In the beginning, he's young, naive, and playful, and seems to win fights partly out of a feeling that he can't imagine losing. And like The Fool from the tarot card, he's definitely willing to jump off a cliff, but figuratively and literally (he can fly, after all). He's lost this somewhat by the end of the series, having had to deal with the losses and suffering he's caused, and having to contemplate the choices he must make for the world.
Rufus and Amberley of The Dreamstone often acted as inept kids in stopping the Urpneys. Nearly everytime however they were handed the victory with barely a hair out of place, either due to the Urpneys own bumbling or some Contrived Coincidence.
Norb of The Angry Beavers plays with this, while he does have Butt-Monkey moments, he is far less often at the brunt of things than Daggett, and sometimes in a very close or contrived manner. This was even Lampshaded in an episode where he and Dag switch roles and Dag notes he (seemingly) avoided a painful injury just like he usually does.
Jimmy Two-Shoes sometimes acts as the fool when he's not playing the Only Sane Man. In Lucius Lost, Lucius divides an island into his side and Jimmy's side, saying everything on his side is his and everything on Jimmy's side is Jimmy's, when Jimmy immediately finds a buried treasure chest on his side. Lucius then steals the chest, only for a bunch of pirates to show up and demand their treasure back. Lucius then tells them Jimmy found it, and they thank Jimmy because they'd forgotten where they'd left it.
Lindsay from Total Drama who is one of the dumbest characters in the show, but is one of the best players, due to a combination of dumb luck and her appearance.
Trevor of Sidekick acts like this in almost every episode. Eric sometimes acts like it too, but not as consistently.
Johnny Test becomes this in 'Johnny & Dark Vegan's Battle Brawl Mania', too concerned with cheering up pet mutant lizard Repto-Slicer to notice Dark Vegan's attempts to kill him. Vegan is outraged to learn that Johnny was completely unaware when he proposes a truce.
Hong Kong Phooey is similar to Inspector Gadget in that he bumbles around defeating villains through either dumb luck or Spot's efforts. He never notices and thinks he beat the bad guys with his martial arts skills alone.
In a world as strange and inconsistent as 12 oz. Mouse, the Peanut Cop always comes off as particularly oblivious. In spite, or perhaps because, of this he is often provides crucial (unintended) aid to the heroes.
Wreck-Gar of Transformers Animated does not seem to have a clue of what he's doing or what's going on around him, but survives frequent lethal encounters due sheer positivity and a general eagerness to help those around him.
Danger Mouse: Ernest Penfold isn't called the world's worst assistant for nothing.
Wander from Wander over Yonder seems to at least be somewhat aware that Lord Hater is supposed to be a villain (probablly because Sylvia constantly reminds him). But whenever he finds him he always attempts to be nice and friendly to him and his minions, leading to accidentally thwarting his evil plans yet again.
Cool McCool is supposed to defeat the supervillains with his skills and gadgets, but usually wins only by dumb luck. He lampshades it somewhat during one of the bridging sequences.