In Substitute School: First Semester, Tatsuki, Orihime, Sado and Ishida have had bangles placed on them by the Gotei 13 to seal their powers, prevent their reiatsu from attracting hollows and make it so their reiatsu doesn't mess with Muggles. They then decide to ask Urahara to remove them. Ichigo points out they are essentially going against an army when none of them are captain class and he can't help because he would side with the Gotei 13. They still persist their point even when Ichigo unloads MULTIPLE reasons why they shouldn't.
Although, it does get a lampshade in chapter 63, when Moody mentions a drug called "Bahl's Stupefaction", the effects of which include causing the user to do extremely stupid things.
Rose Potter, from the Girl Who Lived series, tends to get thrown the Idiot Ball often, due to having special powers that Canon Harry lacked, which would allow her to solve the plot before it even got started, unless she did something entirely stupid. For example, in Rose Potter and the Order of the Phoenix, Rose can control her connection with Voldemort, and knows Occlumency and Legilimency. Thus, she knows that the image of Sirius Voldemort sent her was fake. What does she do? Why, exactly what Canon!Harry did, except she did it in full knowledge that it was a trap. Did she tell Dumbledore, and with him, the Order of the Phoenix? No. Did she, knowing that her going there with a few friends was exactly what Voldemort wanted, and with no reason to take the bait, did she do nothing and inform the adults who wouldn't be playing into Voldemort's hands by walking into his trap? No. She, although she has no reason to, does exactly what Voldemort wants her to do, and is considered smart for doing so.
The cast of Hogwarts Exposed grab the Idiot Ball frequently, but special mention has to go to the scene in which Harry, Hermione and the entire Hogwarts faculty get outwitted by Crabbe and Goyle.
At one point in the Tamers Forever Series the tamers find themselves forbidden from leaving class to go stop some rampaging digimon. Why they did not simply knock the teacher unconscious and run to the rescue anyway is baffling.
Ms. Asaji herself as well, for putting "rules are rules" above the threat of rampaging Digimon. Considering she turns out to be an agent for Takeru, it may have been a deliberate move to force Takato to handle the situation alone and gain more control of his powers.
Lampshaded in Pink Personal Hell And Altering Fate where Pinkie Pie tries to make Dominic laugh and throws flour all over him. He doesn't find it very funny... and tries to wash it off with water, ignoring Pinkie Pie's warning not to.
The Conversion Bureau story called An Azure Future has the protagonist grasping multiple Idiot Balls. After an entire story of wanting to remain human and not undergo conversion, the protaganist pulls a complete ideological 180, joins up with a terrorist organization and helps them successfully carpet-bomb a human settlement, then gases a cop whose only mistake was trying to give him a speeding ticket. Making the whole matter worse, the only reason he decided to help the terrorists was so they would convert him in exchange - something that is their entire purpose to do anyway. Not to mention he could've walked into any of a dozen nearby Conversion Bureaus and had the process done legitimately by trained professionals at any time. He receives nothing worse than mild disappointment from Celestia for the whole thing.
There are a few of these snatched by the protagonists of Calvin & Hobbes: The Series, who are usually quite Genre Savvy, don't always realize that one of Calvin's inventions could completely avert a conflict. Granted, Hobbes is very reluctant to go along with Calvin if an invention is involved, but the other protagonists don't really have an excuse. Particularly egregious is "Nighty Shut Up!", where the solution to Calvin's insomnia is to use the Time Pauser to sleep as long as he likes. This only comes at the end of the episode, while it probably wasn't very hard to figure out at all!
In Ash'sNew Look the titular character thought a place named "Salon Rocket" was a bit suspicious and went in to investigate. He then sees Team Rocket in a Paper-Thin Disguise and asks if they met before. This eventually resulted in Ash getting a makeover by them.
Naruto in That Look at times seems to juggle as many idiot balls as he can find. Perhaps the worst is that he required several explanations to understand why a reservoir that supplies over 70% of Suna's water would be a good military target, despite knowing full well that Suna is in the middle of a desert.
Explored in Blue Sky, wherein Wheatley discovers that he was originally designed to be GLaDOS' idiot ball in an attempt to stop her going genocidal every thirty seconds.