Angel Densetsu raises the Idiot Plot to an art form - the entire concept is that the main character unwittingly becomes the most fearsome gangster in Japan because of the whole cast's inability to communicate properly.
Ao Haru Ride is an example of characters who are so emotionally broken, their personality disorders are so severe, that they cannot help but continuously make the worst decisions possible in order to make their lives miserable and needlessly complicated. Kou Avoids loving Futaba mostly due to his Survivor Guilt, Futaba persistently chooses to be miserable by obstinately chasing after emotionally-unavailable Kou, and it becomes even more absurd by Toma, who knowingly pursues emotionally-unavailable Futaba pretty much because she's emotionally unavailable.
Pretty much every time the Central 46 in Bleach make any kind of decision, horrible things will happen in Soul Society because of their sheer stupidity or Jerkass tendencies. Most of this occurs in Filler of course, but some of it is in the manga and thus canon, which means that all of the Council must be clutching an Idiot Ball.
The ending of Mobile Suit Gundam SEED Destiny hinged on the Minerva crew acting like complete idiots so that they would fight the Three Ship Alliance. The crew ignores Gilbert Durandal creating a fake Lacus Clyne and his plan to control people's destiny. They even let slide the fact that Durandal is willing to use his newly acquired doomsday cannon to blow away entire countries if they don't agree to his Destiny Plan. Actually between all of the characters the idiocy extends to most of the series.
In Mobile Suit Gundam AGE, Nora could have been evacuated in advance if Flit just tell Commander Hendrick that UE is about to attack the Colony. Or if ANYONE in the Earth Federation put two and two together and figure out that UE is going to hit Nora next, something even a 14 years old kid can predict.
Pretty much the entire second half of the Cardcaptor Sakura anime. It's painfully obvious to the main characters that Eriol is the cause of all the weird happenings, but no one is even the least bit suspicious of him. Most glaring is when Eriol buys a huge bag of sewing thread, cryptically says "There are many uses for thread" and wanders off. About five minutes later Shaoran is turned into a People Puppet and forced to attack Sakura with, you guessed it, thread.
Alex "Definitely Not A Villain" Brisbane: Step on the map. Yugi: Make me. Alex Brisbane: Oh, come on. I'll be your friend. Yugi: Look. There's no way I'm stepping on any freaking map. Alex Brisbane: What if I told you there was candy inside the map? Yugi: You've got to be kidding me. I'd have to be an idiot to fall for that. Tea: Candy? That sounds pretty good. Tristan: Yes. Let's go get the candy!
Sonic X takes this to absurd proportions when everyone on the planet fails to remember basic astronomy facts for a couple of episodes, except Sonic himself, amusingly enough. Eggman rigs the moon to block out the sun, making it look like the moon pretty much stopped, along with the sun. Nobody finds this fishy because they've forgotten that the moon revolves around the Earth, and the Earth around the sun, not to mention the Earth spins on an embarrassingly wonky axis. Eggman takes the opportunity to try and brainwash everyone with the lamps he sells, only to have his plan foiled by Sonic yet again, because he was the only one not holding on to the gigantic Idiot Ball. The ball in this case being more of an Idiot Moon.
In the anime of The Pet Girl of Sakurasou, the protagonist is specifically oblivious and thickheaded enough to be continuously embarrassed and ashamed of his female-lead just so hilarity may ensue. By a matter of fact, In the end of the first episode, the protagonist came to a life-changing, self-aware conclusion that he is merely a cog within the machine, a simpleton that is too afraid to be important; and that conclusion — is completely forgotten in the next episode; making it possible to repeat the same mistakes throughout the show, looking for the exact answer he had already answered on the first episode through the many hijinks which ensues with it.
Post exposition, it is explicitly shown that the protagonist has dealt with the tough, socially-inept, probably autistic heroine for almost a whole month; yet he is still shaken by her quirky, eccentric, abnormal behavior as if he just met her.
In The Girl Who Leapt Through Space, Nami's sisters structurally fail to acknowledge her obvious depressed state, going so far as to kick her down even more, as Kazane does in one episode. Even after Nami's Face–Heel Turn, Akiha simply tells Nami to shut up instead of listening to her during their first critical confrontation. Yeah, that really worked, now did it.
.hack//Legend of the Twilight runs on this to an absolutely unbelievable degree to the point that its predecessor .hack//SIGN is genius by comparison. At least in Sign, the main character Tsukasa is trapped in the established game, and can't leave until he finishes despite how dangerous it is. In Legend however, the main characters learn in the first episode that the game they're in is glitched and dangerous, and unlike Tsukasa they have the ability to leave whenever they want to. So what do they naturally do? They continue to play the dangerous game simply because they can. This is exactly why the series was criticized so heavily at this point.
Yuria doesn't want to have sex with Shunsuke because if she does she'll become his life-long sex slave, being a Sex Bot and all. She's pretty sure she doesn't like that idea, even after she starts wondering if she's fallen in love with Shunsuke. That's all well and good, but Shunsuke also doesn't want to have sex with Yuria because he is bafflingly devoted to his chaste, ice-cold girlfriend who he rarely hears from and even more rarely gets to see. And anyway what kind of idiot makes a Sex Bot who is intelligent and emotional enough to decide they don't want to be a Sex Bot? (oh right, that kind).
Simply put, the protagonist has a powerful demon sealed in his balls and can't ejaculate for a month or humanity will be destroyed. He does away with his Porn Stash, yes, and manages to deal with the various Horny Devils going after him, but doesn't stay away from his nymphomaniac-when-drunk coworker.
Which gets even funnier because he does leave her. AFTER the world is safe.
One of the two major conflicts in the final arc of Phantom of Inferno relied entirely on one of the characters coming to a braindead misunderstanding and the protagonist not only not making any attempts to correct her, but saying whatever he could to make himself look guilty and egg on the conflict.
Suzuka would be about a dozen volumes shorter if Yamato didn't find a way to say or do exactly the wrong thing every single chapter.
And on a much larger scale, the only reason there's any plot at all is because the Big Bad apparently never considered personally capturing Naruto before he became powerful enough to challenge him. Given his teleportation powers, it would have been a simple matter for him to snatch Naruto whenever he wanted, but he doesn't actually try until after Naruto gained full control of the Kyuubi's power, and is actually capable of putting up a fight. It wouldn't even have been hard, just pick any of the dozens of times before he got Jiraiya's supervision where he was either on his own, or only with other low level ninja and snatch him. It's not even in his own home village either, it's his JOB to routinely leave the village on little missions with only one mentor protecting him.
Here's your obligatory Hand Wave: It was because Itachi Uchiha was in his way the whole time. Itachi joined Akatsuki to ensure it would not lay a finger on Sasuke or the Leaf. He would have intervened if Tobi tried to attack Konoha in ANY way, shape, or form. That includes going after Naruto. Up until Itachi died, Tobi put on an Obfuscating Stupidity act. When he kicked the bucket, Tobi made his move. However that doesn't explain why he didn't do it before then.
A possible explanation there verges on Voodoo Shark. Every other jinchuuriki was successfully captured without significant resistance by their village because none of them cared that their walking weapons of mass destruction were being stolen by an organization of criminals. The reason Naruto and B were left for last was simply because they were the only ones their respective Kages actually cared about.
The canon explanation is that the Kyuubi has to be sealed last, so it makes sense to leave it last—though, admittedly, that does run the risk of losing the Kyuubi if Naruto is fighting somewhere else and dies (the Kyuubi will eventually be reborn, but after an indeterminate time). It is also established that Tobi wanted Naruto and Sasuke to fight each other first (for reasons unknown, but possibly related to his obsessions— since he is Obito, Naruto reminded him of his old self, so he wanted Sasuke to beat him to prove his old way of thinking wrong...as a wild guess). Its later established that he doesn't need the Bijuu per say, just a certain amount of their chakra, though the full Bijuu is preferred. He manages to get both without capturing either B or Naruto, because sources of their Bijuu's chakra was elsewhere (in a lost limb of the 8-tails and with two deceased villains for the 9-tails, respectively).
Related to this is the Leaf Village's treatment of Naruto. Let's take the son of the Fourth Hokage, who is one of the most revered men in the history of the village, and treat him like shit. That way, not only are we insulting the memory of a hero who died to save us all, but we further the chance of Naruto running away out of disgust and taking his WMD with him to potentially be used against us. Let us also not make any effort to train Naruto in the use of his tailed beast nor actually tell him about it so that he will be completely at the mercy of its influence and unaware that he potentially has a bullseye painted on his back. One or two of these things in isolation would qualify as the Idiot Ball; a string of these things over the course of a decade is an idiot plot.
In the Blood Prison movie, Naruto is sent to prison in order destroy the villain Artifact. However, Naruto was never told about any of this.
"Stink Bomb", from the anime anthology movie Memories is about a salaryman at a pharmaceutical company who takes some experimental pills - thinking they're cold medicine - and becomes the vector for a chemical agent that kills everyone within several hundred meters from him. From then on, everyone just gets dumber. His immediate superiors call him out of a quarantine zone to deliver the pills to them. The JSDF try to kill him, but are so incompetent they just cause massive property damage and only exacerbate the problem. The American military screws things up even more by trying to capture him alive to get access to the chemicals. And throughout all this, the salaryman just can't figure out that he's the source of the obnoxious stink and no one EVER bothers to try explaining it to him. It's played for laughs, but galling all the same.
In Lost+Brain the entire plot is basically one when Fridge Logic kicks in. The plot is based off Hiyama's plan of using hypnosis to remove human weakness with him controlling them having no chance at working, which any amount of additional research would have told him. The plot get even more stupid with the fact that Kuonji and the police never seems to even try to investigate Hiyama even though all the trouble happening can pretty much be linked to him.
Little Jumper would be a lot shorter if Chimari had thought to look up her mother's name before going back in time. But then again, the Idiot Ballis an Ichinose family heirloom.
Infinite Ryvius would have been resolved if they had transmitted what happened to the rest of civilization, and definitely would have if they simply landed or had somebody leave the ship.
In Zeta Gundam a lot of trouble would be avoided if the Argama crew could control the catapult deck traffic better.
The very first arc in CLANNAD hinged on the entire cast failing to have the common sense to question or search out a reason for why one character was being unseen and forgotten by more and more of the school and town. One member decides to investigate alone, and then immediately forgets and becomes unable to see said character. After that, they explicitly avoid this. It's not enough.
Any pre-Unova Pokémon episode is guilty of this, as Team Rocket would show up in every episode wearing easily transparent disguises and the protagonist would always fall for it, then act surprised when Team Rocket tries to escape with their Pokémon. Post-Unova sees the light of day dawn on a loads more competent version of the Team Rocket Trio.
Guardian Force, the latter half of Zoids: Chaotic Century, features a truly spectacular idiot plot in which Hiltz, The StarscreamBig Bad, wants to revive the Ultimate Death Saurer to Kill All Humans until only his race, the Ancient Zoidians, remain. In order to do so, he needs Fiona to open the door to Zoid Eve. The sensible thing to do would be to trick her into doing so at the beginning of the series, when the Ultimate Death Saurer would be unstoppable. Instead, he goes on a totally pointless tangent, building the Death Stinger and using it to go on a seven episode rampage, giving the main characters plenty of time to build the superweapons and develop the skills and experience needed to defeat him. Hiltz didn't need the Death Stinger for his plan; in lieu of the revelations made during the final four episodes, everything which happened before comes across as For the Evulz in-universe, and To Sell Toys out-of universe.
There is however a very good reason why Hiltz didn't simply wake up the Death Saurer ASAP: The heroes have already killed a Death Saurer once before and they can do it again. The true purpose of the Death Stinger was to be a Sacrificial Lamb to power-up the Death Saurer. Given that the powered-up Death Saurer could no-sell a direct hit from the Gravity Cannon, where even the Death Stinger died (temporarily) to it, it is reasonable to assume that the Blade Liger couldn't penetrate the Death Saurer's new armor to hit its core on its own power. The point about the Death Stinger's preceding rampage being For the Evulz still stands, though.
The entire short "break-up" arc in the Sailor Moon R anime could have been resolved by Mamoru telling Usagi the truth. Yes, he had prophetic dreams that she would die if they stayed a couple, but that did not require that he toss her to the curb and dump her. Then it gets resolved when Usagi finds out anyway and he completely caves. The real kicker? The dreams were being sent by the future King Endymion (Mamoru's future self) to try and strengthen the couple's love. That's right — he broke them up to make them love each other more.
B Gata H Kei is a story about a beautiful high-school girl who wants to have sex with one hundred guys. If she could open her mouth and tell anyone that, the plot would have been over in ten seconds. But it wouldn't have been anywhere near as funny. In fact, in one omake chapter her boyfriend loses her memory of ever knowing her, and she still almost solves the plot in about five minutes just by asking for sex.
The Black Knights betrayal of Zero in Code Geass. Several years since the show has ended and it still is the most controversial element of the series. After Schneizel reveals that Zero is Lelouch, former prince of Britannia, and a wielder of Geass, they take his word for it with almost no argument. They then hold Zero/Lelouchat gun point, demanding a confession from him. While Schneizel was technically telling the truth, he was still their enemy, and no one bothered to question whether he was lying or manipulating them. They also don't figure out that their ability to mutiny proves that Zero had not, as Schniezel claimed, Geassed them into obedience.
Every single episode of the Island/Africa arc in Nadia: The Secret of Blue Water. There are so many holes in the "plots", that one could drive a truck through them.
The Cell saga of Dragon Ball Z brought out the worst in most of the main cast. Every step in Cell's progress was the direct result of a protagonist's mistake:
Tenshinhan using his Tri-Beam to incapacitate Cell would, given that it immobilised Cell for a long while, probably have been used to significant effect against Imperfect Cell - who he'd been observing before Cell absorbed Android 17 and transformed. It also took Android 18 far too long to even consider escaping while Tenshinhan was sacrificing his life for her.
Cell wasn't immune, either - giving them ten days training could be reasonably considered a bad move on the off-chance they have some massive power-booster than takes a few days, such as, maybe, a Year Inside, Hour Outside training room.
In all continuities of Area 88, many of the protagonists' problems could have been avoided if Shin had simply picked up the phone and called Ryoko to inform her of his deployment in Asran and Kanzaki's ambitions.
Asran's civil war could have been avoided if Abdael had simply shown King Zak the cryogenic chamber in which Soria was housed and explained why funding the country's medical system was vital to curing Soria's cancer.
The encounter with Death 13 in Part 3 of Jojos Bizarre Adventure could've been resolved halfway through if everyone hadn't suddenly lost their intelligence and were unable to believe that a baby was a stand-user (when they'd already encountered a stand-wielding orangutan, so they've certainly seen stranger things.) Even worse is when Kakyoin figures out what's really going on. Instead of trying to calmly and rationally convince the others (which isn't too much of a stretch because he's already one of the calmer members of the group,) he resorts to hysterics and only convinces them that he's lost his mind.
My Monster Secret is a deliberate example Played for Laughs. The entire series revolves around a bunch of idiots trying to keep incredibly obvious secrets from each other, or making mundane situations spiral completely out-of-control.
In Anatolia Story, one arc involves Nakia arranging for a beautiful peasant girl named Ursula to pose as Yuri in a town where nobody actually met her, all for Ursula/the fake Yuri to be as spoiled and selfish as possible and ruin the real Yuri's reputation. (Not helped by Ursula's Dark and Troubled Past, which made her desperate to have some wealth after having nothing for years.) The trouble is, the plan is short-term at best and hinges entirely on Kail having more important things to do than go out right then and there to deal with the matter. Yuri, meanwhile, does go out immediately... but chooses to do so by riding out on her own, with no proof of her identity or anyone with her who could creditably identify her. As a result, nobody (including, amusingly enough, Ursula) believes her. She does try to meet with the king of the city-state they're in, hoping that he might recognize her, but her plan to get into the palace and meet him fails when she loses her temper at the sight of Ursula's selfishness and, as a result, is basically given a death sentence via being sent to tend to plague victims. Kail, meanwhile, ends the entire thing simply by showing up and confirming which Yuri is the real one. This is lampshaded later, when he says that the entire issue could have been avoided if Yuri had simply presented herself as a princess; this served to show that she had to be more comfortable with the fact that she is, in fact, royalty.
In Fullmetal Alchemist, May Chang is convinced to return home right after the group defeats Envy and reduces him to a mostly-powerless form. Then Scar and Marcoh give it to May in a jar and tell her to take it with her, so she can save her clan by giving the Emperor the secret of immortality. The only secret to immortality this thing knows is the creation of Philosopher's Stones. Not only do these characters think creating them is morally repugnant, May even said explicitly she would not want the Emperor to know it because he would use happily perform the required slaughter. Not to mention that Envy is a manipulative little git who gets off on watching humans kill each other, which they all know from extensive personal experience, and May (for all she is a Badass Adorable) is not equipped to deal with that kind of malice on her own. Once she leaves, it takes about five minutes for it to convince her she should turn right around. The plot required both characters to be in Central for the Final Battle, but surely it could have been done without such a violation of common sense.
Mavis holds the Idiot Ball big time in Episode 175. An odd example where it seems they did care enough to try justifying it, but did it so wrong and backwards it comes off as this. Natsu's ridiculous fight against Sting and Rogue, which many people already hated due to his blatant disregard for apparent strength and his easy curbstomping of a powerful enemy while the rest of the guild had hard times with their challenges, hits the breaking point when Sting and Rogue perform a Unison Raid against him. While Sting and Rogue (the former of whom had easily stomped both Natsu and Gajeel before they decided to get up) begin their Unison Raid, Mavis is going on about how their power is great, but you need more than power to win, and how "these bonds of friendship can't be broken by power alone". The problem with this is that Natsu is the target of her speech, representing friendship and bonds, and Sting and Rogue are the ones representing simple power. Not five minutes before Natsu forced Gajeel on a cart ride out of the fight over a petty argument about Sting's clock position, showing just how few fucks he gives about friendship or bonds, to take on the Twin Dragons alone. Sting and Rogue on the other hand, are A) having inner monologues about promises they made to Lector and Frosch and B) doing a Unison Raid, which explicitly requires the users to be as close a pair as humanly possible for it to work. It'sliterallybackwards.
Lucy. Despite being shown to competently use her magic and her spirits as well as having powerful magic with impressive magic reserves (being able to summon spirit after spirit over and over again is supposed to be significantly impressive for celestial wizards), Lucy continually uses her spirits in the stupidest and most banal ways possible whenever it is actually important. She has also been shown to be able to strategize and think smartly about magic battles, but she will routinely do things that border Too Dumb to Live in sheer stupidity. This is particularly annoying when we've seen many of her spirits being used in inventive and effective ways by wizards who were equal in power or less powerful than she later becomes - used in ways that she witnessed and should easily be able to replicate. A good example is in the Tartarus arc prologue in the first fight against Jackal: he's shown to be able to use his explosions to repel wind-powered attacks, so who does Lucy summon? Scorpio - to use his sandstorm attacks...
The whole plot of Detective Conan kicks off because Shinichi decides that chasing after two shady looking guys in black without bringing any backup (read: the police who were present or the badass martial artist who was his date) with him, or at least telling them what the hell he was planning, sounded like a good idea. The latter could be justified as him not wanting to put Ran in danger; the former, not so much, since going after dangerous criminals is part of the job description for a cop. Of course, Shinichi, at least in the first anime episode, was shown to have been getting a big head from the attention he was getting as a kid detective, so...