Animaniacs gave an aesop very occasionally. But as a cartoon centered around just being silly, the cartoon usually made a point of parodying aesops. They did this (on a regular basis) with their Wheel of Morality, which would provide a random "moral of the story" for the episode that was usually humorous and always had nothing to do with the episode. On the other hand, the movie had a tried and true moral: Never give up, even when things are looking bad.
"Wheel of Morality, turn turn turn. Tell us the lesson that we should learn."
Arthur has about as many episodes with morals as episodes without.
Beat Bugs generally aims to teach one in each episode, themed around a song of The Beatles. "Be Yourself" is one of the most common ones because, after all, "Nothing you can do, but you can learn how to be you in time / It's easy!"
Played straight with Birdz, although they're not heavy-handed since they're often skewed to the avian universe (e.g. Eddie learning the hard way that he should study the map and pack properly during migration season).
Many episodes of 1980s cartoon Care Bears deliver a moral at the end.
Centurions always had some sort of science lesson at the end.
Lampshaded in Danny Phantom: when Jazz is being overprotective at the beginning of "Secret Weapons", Danny tells her, with a bored expression on his face, that "There's a rhythm to these things: ghost attacks, we exchange Witty Banter, I kick ghost butt, and we all go home having learned a valuable lesson about honesty or some such nonsense." This is also a slight breaking of the fourth wall, as it's the basic layout of each show.
Naturally, being a Christian cartoon, almost every episode of Davey and Goliath had one, from not lying to racism.
It takes courage to admit to wrongdoing, especially when you've been led to believe the consequences will be worse than they are. (A Demon in His Pocket)
In order to have friends, you should show that you can be friends with others. (The Starboy)
Having a disability doesn't have to leave you totally helpless; instead, you should make the most of the things you can do. (One of the Guys)
Using drugs as a means of relieving pressure will only mess you up. (The Deadliest Battle)
Before he went to Disney, Doug had An Aesop in almost every single episode. You could tell the Aesop after a couple of minutes already, often even before the episode title.
Although The Fairly OddParents! doesn't have many episodes strictly made to teach a moral, there's one where the moral is thrown in the viewers' faces with a case of breaking the fourth wall: "And sometimes the best weapon of all is to say you're sorry." Cue screen where the phrase MORAL OF THE STORY pops up.
Subverted in Family Guy: While Peter recovers in the hospital, Lois says, "I guess you learned an important lesson." Peter leans back smugly and says, "Nope," at which point the episode ends.
Fat Albert and the Cosby Kids had a heavy-handed Aesop in every episode, driven home by a song from the Kids themselves. One example: "Dope is for dopes/Drugs are for dummies/And if you mess around with them/That kind of mess isn't funny."
Played straight but surprisingly subtle in an animated version of Flash Gordon, Flash alludes to men on Earth who "did terrible things in the name of obedience" but does not name names. In the eighties, this was a clear allusion to Nazi Germany and impressively assumes sufficient motivation, intelligence and education of the kids watching that they would either get the point or go find out.
Parodied in an episode of Futurama. After Fry and Bender drag the Planet Express headquarters along on their joyride in the Planet Express ship, they exit the ship to find the rest of the Planet Express staff, battered and seriously pissed off, waiting for them. Attempting to divert inevitable trouble, Bender says, "And that's how we learned our lesson."
From another episode:
"It's just like the story of the grasshopper and the octopus. All year long, the grasshopper kept burying acorns for winter, while the octopus mooched off his girlfriend and watched TV. But then the winter came, and the grasshopper died, and the octopus ate all his acorns and also he got a race car. Is any of this getting through to you?"
The first three seasons of the U.S. Acres animated series were packed with these.
Gargoyles had the episode "Deadly Force", in which Broadway finds Elisa's loaded gun and starts playing Cops 'n' Robbers. Elisa is busy cooking and not paying attention to him when Broadway accidentally pulls the trigger and shoots her in the chest, nearly killing her, showing just how deadly guns can be. Elisa wasn't even healed in the next episode, either. Too bad it turned into the Missing Episode.
For Henry Hugglemonster: always help your family when they need it. This is a prevailing rule of the show and something that the characters abide by, to the point where if they don't, it is treated as O.O.C. Is Serious Business.
Each installment of The Hive, another Playhouse Disney / Disney Junior show, presents one.
Hunger is a moral fable about a gluttonous Big Eater who goes to Hell and himself gets eaten by a crowd of desperate starving people.
Jem did this in practically any episode about the Starlight Girls — one of them would do something stupid (anything from stealing to drugs) and have to have An Aesop explained to them. A few featured other characters, such as the one where Roxy got screwed over again and again because she couldn't read.
JoJo's Circus has the title character yanked away to a stage with a spotlight at the end of each story to talk about the aesop that she learned from what happened in it.
Roughly 1/3 of all Kim Possible episodes ended on An Aesop (sometimes due to Aesop Amnesia), roughly a third of the episodes ended on a Subverted Aesop, and the remaining thirty took the Aesop and twisted it about as far as possible to create fantastic Aesops, (don't buy mutant toys) Space Whale Aesops, (Eat healthily or your DNA will mutate you into a mini-Hulk) or just outright lampshading them for comedy value.
Lilo & Stitch: The Series from Disney Channel: One of those animated kids shows that works by rote, it's usually a lesson about the power of friendship and tolerance and honesty.
Mack & Moxy has each installment aim to teach viewers something important about social causes, such as preparing for an emergency or helping to feed the needy.
Matchbox Hero City is one of those shows that has a charater or in this case, a car tells himself what he's learned.
Milly Molly had many Aesops, although a few episodes did not have a moral.
The majority of Milo episodes have morals, but a few don't.
My Little Pony: Friendship Is Magic has one of these about friendship at the end of each episode (and therefore on nearly every single page with such a recap), usually given in the form of a letter from Twilight Sparkle to Princess Celestia.
Nina's Little Fables is a short program on PBSKids Sprout featuring fables narrated by show hosts Nina and Star. Some of them are actual Aesop's Fables.
"Space Junk" - "Knowing there's a problem should make you want to help solve it"
"Jet's Time Machine" had a very important one - "You can't change the past, you can only learn from it"
"Sean Has a Cold" - You can have a good time, even when things don't go your way.
Happened quite often in the early episodes of Recess, though they were never in-your-face about it. Then morals came from time to time later on, and season six became Anvilicious.
The Rocky and Bullwinkle segment Aesop and Son subverted not only this trope, but the fables themselves. The titular philosopher would tell a parodied version of his story, say the moral, and then Junior would chime in with a second moral, usually a pun off some element of the story.
On Sheriff Callie's Wild West, each of the show's stories has a moral of some sort that it's trying to teach. However, there seem to be in two in particular that crop up with some frequency:
Don't be afraid to ask for help if you need it.
Be kind and friendly to others and good things will happen. (The town is called "Nice and Friendly Corners" after all.)
Subverted on The Simpsons; at the end of one episode, the family debates what lesson they're meant to learn from the events of the past 22 minutes before finally concluding that it was all "just a bunch of stuff that happened".
This happens in multiple shows; there is an obvious lesson to be learned, but Homer generally interprets it as something completely different.
Played straight in the movie, however. Throughout the film, Homer learns several lessons that causes him to change his behavior. Firstly, by refusing to admit he made a mistake by polluting Lake Springfield, apologize for it and try to fix the damage done, the entire town not only hates him for trapping them in a dome for perhaps forever, but he ends up putting his own family in danger because of it. Secondly, he discovers that by acting out of selfishness and refusing to help save his friends that loved him for years, he ends up alienating his family, who do care for them because of how much they supported them (especially since Ned helped save their lives from the mob that tried to kill them during their escape from Springfield). Finally, he finds out that without his family and friends, not only does his life have no meaning whatsoever, he will live the rest of his life alone, isolated and unloved.
South Park often features an Aesop at the end. Many times Kyle starts a speech by saying, "I've learned something today..." The morals are sometimes humorous - though as often as not - these speeches really are didactic. Sometimes Cartman tries to tell the others what he's learned.
Kyle: Oh shut up, Cartman! You didn't learn a thing! Not a goddamn thing!
Spongebob Squarepants had an Aesop in many episodes in the first few seasons, all of them being important lessons to teach children such as facing the consequences of your actions (Mermaid Man and Barnacle Boy IV, No Free Rides, Squeaky Boots), the grass isn't always greener somewhere else (Nature Pants, Squidville, The Algae is Always Greener), be yourself (Ripped Pants, Big Pink Loser, and again Nature Pants), jumping to conclusions about someone or something can have dire consequences (Sandy's Rocket, Nasty Patty,Wormy), not to curse (Sailor Mouth), not to take advantage of your friends (Can You Spare a Dime, I'm With Stupid and to a lesser extent, Prehibernation Week), and not to touch things that aren't yours unless instructed (Life of Crime). Later seasons tend to lack these.
Robin: Well, I guess this whole experience proves it really is bad to watch too much TV. Starfire: But truthfully, we only prevailed because Beast Boy watches too much the television. Raven: So, there really isn't a lesson here. Cyborg: Yep, it was all completely meaningless. (Everyone laughs)
The whole point of Thunder Cats. Seriously. This was during the time when cartoons where the scourge of the Earth and were corrupting kids (in the same way that Comic Books did before and Video Games are now ... oh wait!), so the producers sat down and said that every episode must have a moral, and they actually hired a child psychologist to help them write the stories.
ThunderCats (2011) continues this out of tradition, with a discernible lesson in most of its episodes.
The Tick also ended most episodes with The Tick turning to Arthur and saying "Arthur, I think we've learned a valuable lesson today," and then expounding semi-incoherently.
The Weekenders loves Aesops. The episode "Listen Up" subverts their convention two-fold by having Carver (instead of the usual Tino) deliver it, and then having him off-center on screen and fading him out, forcing Carver to cut it short.
On What It's Like Being Alone, Aesops are usually provided by one-off characters that are on the verge of death. They then die, violently.
Yogi's Gang: The pilot movie teaches people to take care of their homes instead of simply moving away to look for a "perfect place". Each episode of the series has an aesop regarding the vice represented by the villain.
Young Justice episodes often have Aesops about Leadership, Teamwork or Strategy.