Dollhouse: FBI agent Paul Ballard, who constantly ignores proper procedure, shares sensitive case information with his neighbour, and charges into dangerous situations without preparation or backup. This behaviour got him assigned to the Dollhouse case, and before long it also gets him fired.
Heroes: A dramatic example of an Idiot Hero can be found in Peter Petrelli. He's technically the most powerful character in the show, but the writers have accidentally made him Too Powerful to Live. However this is balanced out by his naiveness and overly trusting nature which ends up getting him and others into a lot of trouble. For example, in Season 2, Knight Templar Adam tricks him into releasing a virus that could wipe out mankind (though Peter isn't aware of it) and despite many characters including people he is close to telling him Adam was evil, he refused to believe them simply because he just could not fathom the idea of Adam being evil simply because he helped him.
This is somewhat justified in-character, as his powers seem to be directly connected to his extremely strong empathy. Hiro acts similar, in that he is an enormously powerful character who acts bizarre because of his childlike nature. In Season 1, we see a version of his character that has matured and Taken A Level In Badass, and it's one of the best plot points.
Shinji Kido, the protagonist, isn't the smartest tool in the shed, and tends to be belittled as a buffoon by the remainder of the cast. Ironically, despite what the description on the main page states, Shinji's intentions throughout the series are to stop the fighting, rather than to enjoy it. Tragically, he does not succeed as each of the Riders die one by one, including himself.
Gentaro Kisaragi, the eponymous Kamen Rider Fourze; he readily admits to being an idiot and gets ludicrously bad marks on tests (the best we've ever seen him accomplish is a 51). Unlike many of his brothers and sisters on this page, however, he already isThe Messiah, with the self-stated goal of befriending everybody, even former Monsters of the Week.
In his later appearance during the crossover movie with Kamen Rider Wizard, we see that Gentaro has somehow managed to become a teacher during the Time Skip. The real shocker is he isn't bad at his job, either.
Revolution: Charlie is this to the point of irritating Miles a lot. In episode 2, she convinced Miles to spare the bounty hunter Jacob, only for Jacob to sell them out to the Monroe militia. In episode 5, she tried following Tom Neville, got caught by him, and Miles had to rescue her as well as make the mission of rescuing Danny harder. This is a Deconstructed Trope, because the trope is played straight and a number of realistic consequences occur. Fortunately, Charlie is becoming smarter, as of episode 6.
Scrubs: J.D. is Book Dumb in anything that has nothing to do with medicine.