Bobobo Bo Bobobo. Most of the "jokes" are Japanese puns, so the English dub appears as a series-long BLAM. It really does make some kind of sense in Japanese, but something was definitely Lost in Translation. It's still a pretty wacky, spontaneous and tripped-out series regardless. It's because of the very nature of the anime that the constant disorientation caused by the altered jokes in the dub never feels out of place.
Cat Soup. It's a thirty minute short film that makes you question the mental state of its maker.
Cuticle Detective Inaba. Let's see... Inaba is a genetically engineered wolf-man who gains superhuman powers by eating hair. His secretary is a sadistic trap, and his nemesis is a money-eating goat who calls himself "The Don." Don's primary minions are a samurai with a bag on his head and a sexy female assassin who spends most of the first episode shooting Don in the head. The page description goes into more detail, which doesn't really help.
Dead Leaves. If you actually managed it this far, go ahead and try to make any sense of the climax.
The opening for episodes in the second season of Death Note, even more so when compared to the first season.
Youko Matsushita, the author of Descendants of Darkness, seems to have had trouble coming up with ideas; as such, her arcs were often heavily cribbed to the point that the style of the work completely changed. The story was trimmed down to essentials and retooled for the anime, and all this hilarity removed. Cracky sequences include:
The 'Catholic boys' school kinky murder mystery of sex and intrigue, caused by a demon, with a side of undercover crossdresser' arc.
The 'Tsuzuki stuck in bad romance novel with a female version of himself as the lead (who winds up with the Expy of one of his male friends)' arc.
The 'the department abruptly competes in Ministry of Hades Field Day and Terazuma is unable to kiss Hisoka even for athletics points' arc.
An abandoned cat was found that an actual vampire decided to give its own blood, which resulted in turning it into a vampire cat named Nyanpire and loving strawberries. Nyanpire later gets adopted and lives with an actual living kitten named Chachamaru. He also makes friends with a samurai cat called Masamunya and an angel cat named Nyatenshi. Masamunya also has a secret crush on him and Nyatenshi will sometimes start flirting with Nyanpire and making Masamunya jealous.
Hamtaro. Even the name of the titular hamster sounds like it was created on drugs. We have things such as hamsters who are everything from ninjas to rainbow creators, a hamster (Penelope) who only speaks in the constant saying of one word (that word being "Ookyoo"/"Ookwee"), and two magical hamsters (Lapis and Lazuli) who reside in a magical Sugar Bowl literally made out of candy. All this and you'll be questioning the collective mental state of the production staff.
Haruhi Suzumiya. A school boy and several others are dragged into a supernatural topics-obsessed schoolgirl's club, and said schoolgirl has reality-warping powers, which could destroy the world if she got bored and decided to make a new one. First-time readers will be left wondering what Nagaru Tanigawa and Noizi Ito were on when they created the original novel.
Also the Hetalia Bloodbath 2010, which starts out as a relatively normal webcast by Finland, turns into a creepy survival story that spawned a truly incredible amount of Wild Mass Guessing, and then the big reveal: the culprits were actually the cat-eared inhabitants of a parallel world where walking around naked is the norm, who need to find a nation with a certain mark on either their chest or butt to keep their world from exploding. In this world there are apparently 123 France's, and America is kinkier than all of them.
In fact, the franchise in general counts. Countries turned into impossibly cute/hot guys with copious amounts of Ho Yay is considered a major twist on Moe Anthropomorphism to most, but many feel the concept of the franchise involved the usage of a fair amount of crack.
Kill la Kill. The story of Ryuko, a tough and plucky wanderingtransfer student who seeks to track down her father's killer and avenge his death, armed with a sentient, super-empoweringSailor Fuku uniform and a giant red half of a pair of scissors that was left behind by whoever killed her father. Her travels take her to Honnouji Academy, a school on top of a huge tower in a city on an island in the middle of a post-apocalyptic Tokyo Bay. Unfortunately for Ryuko, however, her investigations put her right in the firing line of a very hammyAbsurdly Powerful Student Council who routinely execute people for minor rules violations and seek to conquer the planet. And that's the show's basic premise; it just gets more and more surreal from there.
King of Bandit Jing in 7th Heaven. The engine room of the train is one guy singing that causes the dogs to bark at the dodo causing it to run faster. The carnival part is even weirder.
In general, if you are important somehow to the story line, your name is an alcoholic beverage.
At one point in the Lucky Star OVA, the four main girls decide to visit a pet store. After they have looked around, Minoru appears (proclaiming he's Zero) and presents them with a container carrying two frogs that oddly resemble Keroro and Tamama. Their trademark croaking is cuddly at first, until we are treated to gross-out close-ups of the frogs, the croaks becoming louder and more disturbing and the scene becoming more warped. Then, we suddenly cut to the girls in frog costumes doing stuff near a pond. Then, as a final slap to logic, Minoru poofs into being again, dressed as a stage magician, and flies off singing "wa-wa-wa-wasuremono...".
Madlax. Funny enough the director and writer conceived the series ending during an intoxicated brainstorming session.
It's been said that the last half of Neon Genesis Evangelion was greatly influenced when Anno went off his psychiatric drugs, which is also the point where the viewer realizes that the characters have pretty bad psychological issues. Anno also used personal notes about how he was thinking during his clinical depression to add more depth to the story.
Here's some examples of the mad shit that happens in End of Evangelion: a giant robot begins spewing organs and growing extra eyes after being defeated, some more giant robots grow faces (which look like Rei, the show's resident Emotionless Girl) all over their bodies and commit suicide with a spear, with their bodies just hanging in space for a while, a giant version of Rei has a tree covered in eyes (which is actually another giant robot, which is actually the main character's mother) plunged into a vagina in the middle of her forehead (which already has an eye in it), everyone gets hugged by their true love and turns into orange juice while a normal version of Rei watches them (yes, it's a different Rei for each person; there are at least a million of her now), and a giant pink eye rises out of the Earth to kill everyone.
Some of the...odder things in One Piece can lead one to conclude it wasn't only the characters eating magic fruit. In fact, the description for it on the Anime & Manga Widget Series page could also work well here. And to this day, no one has asked Eiichiro Oda the question on if he uses drugs during the making of One Piece.
Oruchuban Ebichu is about a housekeeping hamster who is often beaten mercilessly by her owner. Then there's a guy who's in love with Ebichu.
One of the Pokémon movie shorts, titled Gotta Dance!! might qualify as this. The MacGuffin of the episode is a baton that, when activated, causes every Pokémon within hearing range to start involuntarily dancing. This goes on and off for most of the short, which is both charmingly idiotic and hilarious. Many of the Pokémon shorts that come coupled with the feature length films venture into this territory with their cheerful, idealistic tone, and the fact that nobody is speaking coherently.
Space Patrol Luluco: The writers came up with a 5-minute episode series about a policeman's daughter who is forcefully enlisted and stuffed into a giant gun that fires lasers at (literal) alien citizens. All the super deformity with only (insert low percentage here) the sex-appeal.
Urusei Yatsura features such things as Lum (an alien) assembling together random fossils and turning them into a living creature and Ataru summoning the devil by having a rather strange jogging route. Then the anime adaptation and the movies bring it Up to Eleven, the top of the weirdness being reached with the second movie (that, to be fair, was set in a dream) and episode 151. In fact, Rumiko Takahashi could have her own page for this trope.
The So Bad, It's GoodYaoi manga series Vibrator Company starts with a pair of salarymen, employees of the titular company, breaking into a warehouse full of sex toys and exchanging vibrators as a token of their love for one another. This is probably the least ridiculous thing that happens - from there on in it's a nonstop crazy train of suggestively-shaped office buildings, security guards dressed as teddy bears and industrial espionage. Over sex toys.
The fourth and final season of Yu-Gi-Oh! GX. It is a combination of a Coming-of-Age Story for all its main characters, as they choose what to do with their futures once they leave Duel Academy, and an Assimilation Plot orchestrated by the incarnation of darkness and despair, which in turn was picked up from an abandoned plot line all the way from season one. Overall the result is quite the Mind Screw.
Pop Team Epic. Every single episode feels like the animators OD'd and somehow lived to tell the tale before coming up with them.