Sakura Kinomoto of Cardcaptor Sakura plays with this. In early episodes she was something of a Naïve Everygirl, childlike but fairly normal in terms of her age's intelligence and demeanor. In later episodes she is something of a Genius Ditz, highly developed in her handling of her cards and even the odd bit wisdomic, but an exagerratively naive Kindhearted Simpleton in most other areas.
Light Yagami. He goes from erasing his own memory, trusting in the brilliance of his planning to ensure L's death while cementing his own complete innocence... to hiding the Death Note in storage and really hoping no one finds it while he's not looking.
The whole Mello and Near arc has Light nerfed down hard, making great mistakes apparently to balance the odds of the two kids-nemesis. He loses the note, he loses Sayu, he loses his father... and one of his "best" responses is to confirm to Near he's Kira by sending a mass of stupid people at the exact location (and only there) of Near's anti-Kira organisation with the great expectations that they'll lynch someone of L's level. An extended period of complacency between arcs with no intellectual rival, and belief in his own hype likely have something to do with it, as does the fact that Near and Mello have far more information to work with than L did.
Dragon Ball Z: Cell appears to lose brain cells the stronger he gets. Compare Imperfect Cell with Perfect Cell. While Imperfect, he's The Chessmaster and a No-Nonsense Nemesis who constantly ran circles around the Z-Fighters and outsmarted them on more than one occasion. While Perfect, he's an arrogant, egotistical jackass of a Smug Super who makes the exact same mistakes he had previously mocked Vegeta and Trunks for making, such as deliberately angering Gohan enough for him to unlock his hidden power for the sake of a good and challenging fight and Hulking Out without maintaining his speed. It's so bad that Goku of all people could play him like a damn fiddle.
Alphonse in the 2003 anime version of Fullmetal Alchemist. He starts off as an intelligent, insightful young boy who was the sensible one compared to Ed. Later on he makes many very poor, and arguably stupid choices like taking Barry the Chopper's mind games to heart, and distrusting people who he's known all his life. This happens in both the manga and anime, but in the manga, Al learns from this and doesn't do anything like it again. In the first anime it mainly takes effect in the later half,where he runs off every time he gets upset, even though the Homunculi and Dante are looking for and trying to kill them, going along with Shou Tucker's plans and not telling Ed (even though Tucker made his daughter into a chimaera, resulting in her death, and letting Sloth convince him that she's his mother, even though she is a Homunculi when Ed is trying to remind him that they're fighting for their lives, immediately running towards Envy disguised as Winry, right after Ed says it isn't her, and barely putting up a fight. He arguably became more impulsive than his brother, whereas earlier in the show it was the other way around. This could be interpreted as the writers having Al act more like how a real little boy would if they were put in such a situation, but he becomes more competent again in the finale. Other than that he basically becomes quite the load.
As of late, whenever Naruto seems to start growing as a character, he immediately takes a level in dumbass. Most notoriously when he doesn't realize anything is wrong during the attack on turtle island by Kabuto and zombie!Deidara. Despite the living island suddenly acting as if it were hit with a high-level earthquake.
For a long while, Sasuke from the death of Itachi and throughout the succeeding arcs. Even after both Tobi and Itachi had both implored that the destruction of Uchiha clan wasn't the fault of the Leaf, he decides to screw everything and try to destroy the Hidden Leaf village and every single person living in it, despite Itachi's intentions and words told by the main antagonist of all people himself urging the very contrary. All the while, his chakra grows noticeably darker and colder through his hatred, implications seeming as if he's forcing himself to hate in order get more powerful. At one point, he impales Karin when held hostage with the Chidori, despite Danzo holding her in a position where his body and head is in clear sight of his lightning-fast attack and discards her for being "useless".
Arguably Luffy of One Piece. He was never a genius by any account, but he seems to have gone from "not bothering to understand what people say" to "not able to understand what people say" in some cases. He also showed at least some insight at the start of the series, like realizing how he could make Coby join the Marines and calling Vivi out on how it's naive to hope that nobody will die in a war. He has not really had any of those moments for a long time. However, it may be justified in that Luffy is not good at anything but fighting and socializing. At the start of the series, he had a very small crew and thus had to handle several tasks himself. Nowadays, his bigger crew of eight members handle all the practical things for him, and in return he beats all the bad guys they don't have a chance against. So when he does not have to use his brain, he probably has made it a habit to switch it off most of the time. It's noteworthy that when the crew was split up, and he was on his own, he did seem a bit more intelligent and thoughtful, but when he gathered some new allies who could do the thinking work for him, he returned to his usual ditzy self.
Pokémon: The Team Rocket trio. In the early appearances they are very competent, albeit very hammy, and have succeeded several times in stopping the heroes and capturing Pikachu only to be save by a Big Damn Heroes moment or an Ass Pull of some sorts. Fast forward and their only real purpose now is to show up, provide comic relief, and blast off again, barring the episodes that focus on them being sympathetic to the point where they might as well not be villains if not for status quo getting in the way.
However, they eventually reverted to being comic relief villians.
Ash himself has zigzagged this trope and Dumbass No More throughout most of the seasons; putting the fully experienced, competent and intelligent trainer he ends most seasons as into the next season - where he's expected to go through the early rookie stages again - would kill all drama as he would utterly destroy the Gym Leaders and rivals. Ash deposits not only his Pokemon but his brain cells at Professor Oak's house and goes off to the next region to make mistakes a five-year-old would avoid.
Ranma ½: Genma. At the beginning of the series, he's lazy, doesn't think things through, and isn't the brightest bulb on the circuit, but is for the most part a competent martial artist who, despite some (admittedly quite serious) blunders, has trained his son to be an incredibly skilled martial artist. As the manga goes on, he becomes increasingly stupid and incompetent, with only one bright spot during the Ryu arc.
Actually worse in the English dub as they removed her character quirk of mixing her proverbs up in the first season and give her a voice actress with a leader style voice then Sailor Moon S came where Venus's ditzy personality had completely taken over and the English dub just so happened to give her a new voice actress that emphasized this personality.
The degradation arguably occurred before that, considering how Gourry's dumbass swordsman persona was apparently all an act in the original novels.
Tenchi Muyo!: Mihoshi, especially in Tenchi Universe. Somewhat justified in the case of Tenchi Universe (and Tenchi in Tokyo) since those aren't actually the same Mihoshi, due to those being alternate continuities. Totally unjustified in the 3rd installment of the OVA series, though.
In the original series Yatterman, Gan is somewhat naive, but not stupid. The remake makes him a bit more careless but still rather smart. The live-action movie, however, turns him into a total Idiot Hero.