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Sgt. Schultz from Hogan's Heroes. Played with in that he was actually on the prisoner's side, or at least genially corrupt, from the very beginning.
Jason Stackhouse from True Blood. Partially averted, though: although he's frequently Too Dumb to Live and always ends up all right in the end, he's more of a Karma Houdini than most Fools: he's frequently selfish, amoral and religiously intolerant. Although he does sometimes get his comeuppance (the priapism and being accused of some murders), he does always seems to come out fine in the end by no other reason than dumb luck.
Played with in Firefly. While most fools are depicted as happy and childlike, Jayne Cobb, easily the dumbest member of the cast (despite his talents for interrogation) is also grouchy and generally unhappy.