Groo the Wanderer is probably the biggest example of them all. He's the greatest swordsman in the whole world... and the dumbest as well. Barely capable of feeding himself, Groo brings bad luck wherever he goes and has a bad habit of decimating whole towns and cities, often as a result of trying to help the local residents. Nearly every comic ends with him being chased by an angry mob while he tries to figure out why. He's so notorious for causing destruction that, in one instance, simply passing near a town causes economic collapse and a massive riot when the news of his arrival circulates.
Deadpool may count as a rare example of a non-goodhearted version of this trope.
Sam & Max: Freelance Police: Both to some degree. Especially in the comics, where most of their cases are solved by luck. Sam is a little less of a Fool in the adventure games, where the game play relies on him having at least some idea of what he's doing, but Max rarely does.
Zayne Carrick from Star Wars: Knights of the Old Republic is The Fool personified. Not only is his unique force power directly stated as causing "unexpected changes in fortune" (and note that he is considered incompetent by everyone who does not recognize this), but he is referred to as "The Fool" by several powerful people, nearly all of whom are trying (unsuccessfully) to kill him.
In his earliest incarnation, Johnny Thunder was an insanely lucky guy due to having been born at 7 AM on 7/7/17. A Saturday, the seventh day of the week, no less. (Yes, born in 1917; he goes way back.) By pure luck alone, he'd accidentally demolish enemies while his actual attempts to hit them missed completely; sometimes he didn't even figure out that he was being attacked because they'd take themselves out just outside his field of vision. Also, he was connected to a genie called the Thunderbolt who was like his guardian angel, summoned by the magic word cei-u. Of course, Johnny had no idea of this, but would often yell "say, you!" at whoever he was chasing and accidentally summon him. (How good as he at accidentally tripping up his foes? The Thunderbolt wasn't in every appearance! He could solve crimes on his own via dumb luck without any outside help.) Unfortunately, his phenomenal luck wasn't enough to prevent his Aloof Ally, a lovely blonde by the name of Black Canary, from taking overhis spot as the backup story in The Flash's comic.
He still exists, but as it is with The DCU, there's been retooling and re-re-re-tooling.