Static Shock had many Very Special Episodes, including "Sons of the Fathers" (focusing on racism), "Frozen Out" (focusing on homelessness), "Jimmy" (focusing on school violence), and "Where the Rubber Meets the Road" (focusing on dyslexia).
Mercilessly spoofed in Drawn Together, in an episode appropriately named "A Very Special Drawn Together Afterschool Special". Started as a roleplay by the housemates to help Xandir decide how to inform his parents of his homosexuality, the effort quickly derailed, which resulted in nearly all of them getting killed by the end of the episode.
Also lampshaded in an earlier episode: ("Hi, I'm Toot Brownstein... In this episode, we awkwardly dealt with eating disorders.")
Gargoyles has two major Very Special Episodes, but tended to buck the trend by showing aftereffects in later episodes:
In "Deadly Force", the dangers of playing with a loaded gun are looked at, including a description of the path the bullet took inside the victim's body. The message may have been too graphic, however. It was initially banned from reruns due to its heavy subject matter. When it returned, the scene of Elisa getting shot was edited in such a way that the viewer could no longer see her bleeding while lying on the ground. In any case, it forced Broadway (the shooter) to mature as a character; he was initially a fan of violent cop shows and movies, but after this experience grew to prefer investigative work. His hatred of guns in this particular episode is tied directly to his personal guilt, rather than guns being wrong inherently. And, as a nice touch, Elisa spent a few episodes on crutches as she recovered; and - having noted that she shouldn't have left the gun out in the first place - was later shown making sure to keep it locked up.
Then there's "Lighthouse in the Sea of Time", the episode concerning illiteracy - though the gargoyles came from the Middle Ages, where the ability to read was very uncommon, it's still a little hard to credit a plot where the villain wants to throw away the personal diary of Merlin, and is stopped by heroes, who then deliver a speech about how stories are treasures. (Admittedly, the villain was just frustrated that Merlin's writings didn't include any magic spells, and quickly calmed down.) Again, Broadway's the one who got the major Character Development, becoming quite the fan of William Shakespeare - just look at that moment when he describes Castle Wyvern's kitchen, and then his eyes really light up when he describes the library. The blind author introduced in "Lighthouse" also becomes an occasionally recurring character.
Nickelodeon's As Told by Ginger was, as far as Nicktoons go, never one to shirk away from touching on real adolescent issues. Three notable episodes stand apart for their efforts to address particularly tough subject matter: "Stuff'll Kill Ya" (about caffeine addiction), "And She Was Gone" (about depression, suicide, and how schools overreact to students who are allegedly depressed or suicidal by assuming what they write is a cry for help), and "Losing Nana Bishop" (about death and coping with loss). "And She Was Gone" was nominated for an Emmy Award in Outstanding Animated Program (Less Than One Hour).
The "big 3" American networks united to air the special Cartoon All-Stars to the Rescue, where cartoon characters from Looney Tunes to Teenage Mutant Ninja Turtles try to teach a child called Mikey about the dangers of marijuana. Ludicrously. The point that breaks Mikey, other than his addiction forcing him to steal from his little sister and his family worrying about him, is that marijuana will turn him into a green-skinned zombie; it's quite obvious where Mikey's priorities are, and it's made even worse when you consider most marijuana users aren't, y'know, zombies. Stupidest of all is that cartoon characters who really have no business knowing about drugs are the ones preaching to Mikey, such as Huey, Dewey and Louie of DuckTales, Alvin and the Chipmunks and, of all people, the Muppet Babies. And seeing Bugs Bunny talking about a joint is really quite ironic, considering that Bugs Bunny and the rest of the Looney Tunes did NOT start out as children's cartoon characters (it was made that way through erroneously packaging and syndicating the classic Warner Bros. cartoons as children's entertainment). Its first US airing began with a live statement from then-President George H.W. Bush and his wife Barbara, while airings in other countries similarly began with live statements from their respective heads of government.
Captain Planet is one big Very Special Show, telling children to not cause pollution (despite rarely going into why people polluted in the first place). However, it had many particular episodes that focused on more down to earth problems that children, teenagers and young adults may face. One of these was a drug episode "Mind Pollution" where Linka's cousin gets addicted to a designer drug called "Bliss" created by Verminous Skumm (who appeared to specialize in "pollution of the body" in the show, so to speak). Another episode was about AIDS, involving Skumm spreading lies about a young AIDS sufferer such as the virus could be contracted just through casual contact (it also had implications that the AIDS sufferer was gay and in love with his friend, who was defending him from being bullied). The former episode is at least somewhat notable for breaking the Never Say "Die" rule by showing Linka's cousin die from throwing himself out the window and bleeding profusely.
Then there was the episode where Wheeler in a dream discovered an island inhabited by greedy, foolish humanoid mice who refuse to stop having large families. Initially clueless American boy Wheeler is against government mandated population control, but he learns his lesson when the humanoid mice overpopulate to the point that their island destroys itself.
"King Scoopa Koopa" focuses on nutrition and obesity, with capitalist greed thrown in as well. King Koopa opens a fast food stand and the cave people are immediately hooked. Mario, Luigi and Yoshi visit the stand and enjoy the food so much that they gain a considerable amount of weight in one sitting. Princess Toadstool forces them to go on a diet, with Mario the only one to successfully wean himself off the food. Luigi and Yoshi aren't so lucky, as the food mutates theminto Chickadactyls. The episode also touches addiction when Luigi and Yoshi steal Toadstool's treasure chest out of desperation and trade it to satisfy their cravings.
In "Born to Ride," which centers around street gangs and peer pressure, Yoshi runs away from Dome City after being yelled at by the Mario Bros. He finds the Dino Riders, a motorcycle gang, who "initiate" him after he unwillingly vandalizes a cave person's house. They successfully exploit Yoshi's child-like personality to kidnap Mario and Luigi as ransom for Koopa. Yoshi eventually catches on and saves his friends but not before the Dino Riders give one last chase.
Disney's Doug played it straight in the episode when Patti Mayonnaise thinks she needs to go on a diet after lagging behind in gym class and overhearing Doug talk about her weight problem (in reality, he was talking about how big his Lucky Duck Lake monster lure is), but ends up purposely starving herself to the point that borders on anorexia. Considered one of the more highly-regarded episodes from this era of Doug.
Parodied on Powerpuff Girls in one episode where Blossom ends up being the perpetrator of a crime (namely, stealing a rare and expensive golf club set for the Professor). The episode title, "A Very Special Blossom," alludes to the Mayim Bialik sitcom Blossom on NBC, where practically every other episode was a "A very special Blossom."
This was played straight in "Equal Fights" (focusing on sexism) where the town is terrorized by a feminist villain called Femme Fatale, who tricks the girls into hating boys with her propaganda. Ms. Keane and Ms. Bellum manage to bring the girls back to normal and they take Femme Fatale to jail after telling her that she has no idea what she's talking about.
"The Great MacGrady" has the kids finding out lunchlady Mrs. MacGrady has been diagnosed with cancer. It was dedicated to its writer, Leah Ryan, who passed away from the disease, to the point where Mrs. MacGrady's name was changed to Leah (it was usually Sarah) for the episode.
Another VSE that comes to mind is the one where the show's resident Butt Monkey George is diagnosed with dyslexia.
A very strange case in an episode where there's a candy bar that makes sparkles come from your mouth that Buster covets. George and Fern keep eating it. The metaphor gets more obvious as Binky buys every piece from the local stores and becomes a sort of dealer, with George and Fern being regulars and going as far as to constantly buy from him despite him being a more expensive middle man. And then George and Fern are shown tired and depressed when they don't eat it. It seems to be a shallow drug metaphor, or at the very least an episode warning the dangers of addiction... until Buster investigates what the candy's made of, and finds out that it actually contains drugs. The effect is even illustrated, with the candy's "secret ingredient" attaching to the brain and making the consumer feel really good, until the material breaks down and the consumer feels really depressed and wanting more. Overall, the real Aesop seems to be about the lengths Corrupt Corporate Executives will go to get money. It ends with Buster's mom exposing the candy in the news.
Another episode featured George befriending a rabbit named Carl, who happens to have Asperger's Syndrome. The episode deals with George learning about Asperger's and autism in general. Unlike most VSE's, however, Carl has shown up in later episodes.
One infamous episode titled "Bleep" featured DW learning a "swear" word and accidentally causing other kids in her class to say it. Rather than explaining that certain words may be considered offensive or rude, DW's mother basically says "It means I want to hurt your feelings". Not helped that the swear word is never given any context as to its meaning.
Yet another episode featured the Tibble Twins becoming obsessed with a Power Rangersparody series. The episode centers around the twins pretending that everything (including school) is part of the show's world and that they are the main heroes of said show. It ends with the twins hitting DW with a swing causing her to need stitches on her lip and learning two important lessons. First being that there's a time and place for playing pretend and that real life comes first. The second being that not everyone might want to play the same game as you, and that you should never do something that might hurt them.
"April 9th", which was made in response to the 9/11 attacks, dealt with the students dealing with the aftermath of a large fire at the school.
There's also a hilarious episode that sends up the VSE where the boys are forced to join a choir class whose teacher (voiced by Jennifer Aniston) is using them to spread the message of saving rainforests. When the group gets lost in a rainforest and nearly killed by everything but the kitchen sink, the teacher snaps and screams "That's it! F**K rainforests!" and proceeds to change their message to destroy them rather than save them. The whole thing caps off with a PSA urging viewers to help "join the fight to destroy all rainforests before it's too late." While the anti-environmentalist message may make viewers angry or upset, you have to admire the balls it took just to say that, when most other shows would go the pro-environmentalism route.
South Park also has the anti-bullying episode "Butterballs" that features Butters getting bullied by his grandma and played out like a schoolyard bullying story. It's not Played for Laughs in the slightest, though it does have its own subversion in the form of parodying anti-bullying programs when Stan's attempt at such a film goes south. The overall message of the episode is "Bullying is bad, but exploiting the victims of bullying for fame, money, and admiration is worse."
"Eat, Pray, Queef", one of the show's more Anvilicious episodes, played out like a 20-minute women's rights tract. However, it's hard to tell if it's a sincere pro-feminist message or a parody of it. It might be the latter, considering that Trey's track record with women includes an abusive sister and an unfaithful ex-fiancee.
Parodied in "Sexual Harassment Panda", complete with a closing Public Service Announcement against suing people to make money.
Beavis And Butthead had one called "A Very Special Episode" where the duo find a baby bird (or as Beavis calls it, "a chicken nugget") and nurse it back to life. By complete accident, as in typical B&B fashion they actually wanted to see it die. When the two manage to restore the bird by feeding it, they actually thought that the bird would automatically die only after they fed it. They were told by the nurse that the bird was gonna die anyway no matter how much they try to help him. Of course, being stupid as they are, they thought she said to feed so it can die.
Batman Beyond had so many teen drug episodes it's hard to call them "very special", but they all have that tone to them that makes them seem to count. Then again, one of them was a 'excessive fashion statements = drugs' episode, and one of them was a 'video games = drugs' episode. And then there was the 'adoption / stalking' episode. And a couple of bullying episodes, although those are more just an excuse to have someone ELSE Terry knows from school go insane in a way that involves Batman.
Family Guy has some. Most of which are parodies, and some of which are serious:
The simply titled "Brian & Stewie" (the 150th episode, the only episode in which Seth MacFarlane is credited for doing all the voicework, and the only episode in which there are no cutaway jokes, flashbacks, or Take Thats against whoever's famous) where Brian and Stewie are locked in a bank vault for the entire weekend and Stewie discovers that Brian has a gun in case he wants to commit suicide. Sure, there was that really gross poop-eating scene and some musical numbers at the end (which only aired because FOX had some gimmicky music-based episode line-up on Animation Domination, which explains why The Simpsons episode "To Surveil with Love" had that opening with everyone in Springfield lip-synching to Kesha's TiK ToK. In all reruns and on the DVD, the musical numbers aren't there), but other than that, the episode was a serious look at the relationship between Brian and Stewie.
Another episode ends with this parody of what's found at the end of "very special episodes": "To learn more about drugs, go to your local library. There's probably someone behind it who sells drugs."
Parodied in the episode where Happy-Go-Lucky Toysnote The toy factory Peter used to work at before his boss died is merged with a cigarette company who uses the place as a front to get kids hooked on tobacco. First, it's played straight, with Peter enjoying the perks of being a company head and backing up his superiors — until Stewie starts smoking cigarettes, then Peter protests against them. In the end, the message was really about how it's wrong to kill strippers (a Call Back to a short scene where a Senator is freaking out over killing one of the dancers at a D.C. strip joint called "The Oval Orifice" and Peter calming him down by saying that, yes, choking her to death on dollar bills and beating her with a chair were horrible ways for her to go, but at least she didn't die of cigarette smoking), because strippers were put on Earth to entertain horny men and most of them are already dead on the inside from the life decisions that led them to this point, so physically killing them is redundant.
"Screams of Silence: The Story of Brenda Q.", aside from the traditional Black Comedy moments, was actually a very serious episode that dealt with Quagmire's sister being abused by her boyfriend (which was first mentioned in "Jerome is the New Black"note The episode featuring Quagmire calling Brian out on being a pompous asshole who pushes his atheist and liberal views on others), and is one of the few (if not only) times that Domestic Abuse is actually shown in a serious light on the show.
Earlier in the series, there was an episode where the Griffin family meet a family of nudists (Peter saved the father from being swept in an undercurrent while fishing, thinking he lost his trunks in the water). Meg ends up dating the son, and the family aren't too comfortable with that. They eventually warm up to the idea, even exhibiting their own tolerance for the practice by going nude when he comes over. Despite the ruthless amount of innuendo and situation gags, it's really quite touching.
"Brian Wallows and Peter Swallows" had some funny moments, but was really a very special episode (and one of the few episodes, according to Seth MacFarlane and Alex Borstein, that actually has human emotion in it) about coping with loss (Brian caring for the elderly shut-in who used to be a jingle singer and Peter caring for the baby birds that have nested in his newly-grown beard).
Parodied at the end of an early episode in which The Griffins go to an Indian casino and Peter and Chris go out in the woods on a spirit quest. After Stewie makes a racist comment about Native Americans, Lois launches into a "The More You Know" PSA about how Native Americans are people too (followed by Stewie stating the same thing about Mexicans, Meg saying the same thing about Swedish people, and Peter bashing Canadians, and concluding the episode with "Canada sucks!")
"Livin' on a Prayer" was about Lois kidnapping a baby so it can be given cancer treatment much to the disapproval of his Christian Scientist parents, who don't believe in letting doctors treat illnesses.
The banned episode "Partial Terms of Endearment" was actually praised for showing realistic arguments for and against abortion — and, at least until the end where Peter flat-out tells the audience that the baby Lois was carrying was aborted, treated the subject matter with respect. No wonder it was banned from American TV (it is available on DVD and UK viewers have seen it on BBC3).
Even The Simpsons trotted one out, in the form of the episode "The Color Yellow." For Black History Month (which is celebrated by Springfield Elementary despite the fact that the has a low African-American population), Lisa - at first reluctantly, and then with increasing interest and obsession - investigates the mention in a 150-year-old Simpson family diary of a slave named Virgil. It eventually comes to light that Lisa's great-great-great-great-grandmother, Mabel, had helped Virgil to escape to Canada - and then married him. Grampa mentions that Mabel and Virgil's son was his great-grandfather, which makes Bart and Lisa one-sixty-fourth African-American. Marge wonders why this had been a family secret so long, pointing out that no one had ever complained about the family having French ancestry. Grampa's answer is that Homer's paternal side of the family is very racist and wouldn't have tolerated a black relative, much like Homer doesn't tolerate Marge's French side of the family.
The Emmy-winning "Homer's Phobia" has Homer making a new friend named John (played by guest-star John Waters), but when John turns out to be gay, he's horrified and Marge calls him out for it. Things get worse when Homer thinks Bart will end up gay because John spends more time with Bart than Homer does (and even begins wearing Hawaiian shirts and dancing to 1950s music while wearing a wig). Homer tries to "cure" Bart by taking him to a cigarette billboard (which is for slim cigarettes), a steel mill (that turns into a gay disco after the work day is over), and a hunting lodge (which fails). At the end, Homer learns to accept Bart for who he is, and Bart doesn't know what Homer is talking about until Lisa spells it out for him: "He thinks you're gay."
"The Cartridge Family" is an odd version of the very special episode. For one thing, it was a shift from the original set-up (which has The Simpsons trying to survive a soccer riot that erupted in town). For another, it was a big Series Continuity Error as Marge had a gun before on the episode where she becomes a cop and Marge never complained before about Homer having guns in the house note though most of the other guns Homer had were shotguns and rifles, and the gun Homer had was a handgun, which can easily be mistaken for a toy gun and is more likely to be misused by the children. For a final note, Homer learns his lesson about guns (and lying to his wife), but Marge ends up with the gun after seeing how good she looks with it, which leads to a Broken Aesop of "Yeah, guns are dangerous, but they make really good fashion accessories."
There was one about gender equality where Penny joins the football team, one where Penny greatly misuses her credit card, and an anti-piracy episode. Even the Christmas Episode kinda counts, since it was part Christmas and part the Proud Family learning about Kwanzaa, and subsequently learning to appreciate their heritage more.
Fat Albert had many of these, including episodes centered on smoking, homelessness, gun safety, pedophilia, stealing, racism, going to prison, etc.
The American Dad! "The American Dad After School Special" focused on body image and eating disorders. When Steve falls for a chubby, Perky Goth named Debbie, Stan is appalled to find that Debbie isn't the skinny, model-cheerleader-popular girl-type that Steve always lusts after (with hilarious results), but rather than Debbie succumbing to self-esteem issues because of her body, it's Stan who does after Hayley and Klaus call him out on being meaty himself.
A lot of episodes of American Dad! (according to the DVD special about the creation of the show, seen on the volume one DVD set) can be seen as deconstructive parodies of the "very special episode" in which all conventions and expected twists, turns, and plot points seen in a "very special episode" are either mercilessly subverted, mocked, or played out realistically. Case in point: "A Jones for a Smith" (the episode where Stan becomes a crack addict). At the end when Stan is rehabilitated, Francine is the only one happy that he is cured, Steve is pissed at Stan for ruining his chances at hooking up with a hot high school virgin who is attracted to nerds (and whose father is willing to let Steve sleep with her), and Hayley is begging Francine to let her into rehab for her marijuana problem (with Francine ignoring her).
Completely parodied in the Animaniacs episode, "A Very Very Very Very Special Show". The Warner siblings try to win a humanitarian award, so they preach throughout the whole cartoon about smoking, violence, sexism etc. Once the award goes to a different cartoon, the Warners instantly revert back to their normal selves and go against everything they were preaching.
Played straight in "One Flew Over the Cuckoo Clock", which features Slappy Squirrel going insane from watching too much daytime TV and getting put into the hospital. This eventually results in Skippy being taken away by a CPS agent. The whole thing reminds one of an older relative going senile, seeing how it was based on Tom Ruegger's memories of visiting his aunt in a nursing home.
The Pinky and the Brain episode, "Inherit the Wheeze" deals with the dangers of smoking and has a cigarette addicted Brain working along side a corrupt tobacco company. He does speak against the company at the end.
The Rocko's Modern Life episode "Who's For Dinner" has Heffer learning he was adopted and coming to terms with the fact.
The Hey Arnold! episode "Big Bob's Crisis" has Bob suffering a heart attack.
"Helga on the Couch" centered on child neglect and how bullies become bullies. The episode didn't explicitly touch on the subject outright, but given Helga's depressing story, it might as well be about that.
Jem had one about a girl named Laura Halloway, who was brought to the Starlight House following the deaths of her parents in a car accident. Still reeling from the tragedy and feeling that no one really understands her, Laura meets another student named Bobby, who gives her drugs claiming that they'll make her feel good and help her play the guitar better. As a result, Laura hallucinates, nearly jumps from a high window believing she can fly, gets insomnia, keeps the whole house up with her horrible guitar playing, and generally acts like a jerk to everyone. Only after she gets caught stealing from Jerrica's purse and after she sees Bobby going after Ashley with the same lines he used on her, Laura goes to a support group meeting at Jerrica's suggestion and begins to recover. At the end of the episode Laura and Ashley help the police catch Bobby.
Nina Needs to Go! is an entire show about toilet training.
Another Disney Junior short series, Shane's Kindergarten Countdown, had an episode about this.
Sid The Science Kid had "Getting A Shot: You Can Do It!", about Sid's grandmother, who's also a nurse, coming to school to give the kids a flu vaccination. The kids then learn, sing songs, and play games about the flu vaccination's benefits.
While not in the same vein as most other VSE, A Pup Named Scooby-Doo had one episode where the gang deals with a headless skateborder ghost. As they're putting the clues together, they discover a cache of drugs which earns disapproving tones from Velma and Scooby (Velma says the word "drugs" with plenty of venom in her voice while Scooby responds "Drugs? RUCK!") In the end, they find out that the ghost was a former skateboarding champ who had been disgraced for using drugs.
The Centsables: Downplayed, but every episode features some surprisingly dark moments of subtext such as "vitamins" being used to make a character feel adequate in life, running away with a "child-like genius" to get a perfect life, identity theft gangs, and pretty decent people willing to look the other way for one reason or another enabling crime to happen.