Never Grew Up

As you know, Growing Up Sucks. Some children, however, have found a way to halt their aging at childhood via Applied Phlebotinum or some supernatural means. Most of the time they'll have the mind, emotional maturity, and/or sensibilities of a child as well as a prepubescent body; adults in children's bodies are more likely to find it inconvenient or downright sucky, although not always.

Yes, Peter, people grow up outside of Neverland.

Compare Really Seven Hundred Years Old. Not to be confused with Adult Child. When the same effect causes hardship and angst for the eternal child, it's Not Growing Up Sucks. When an attempt is made to impose this on a real-life child performer by the production team of a program he's in, it's Not Allowed to Grow Up.

Examples of Never Grew Up include:

Anime and Manga

One episode of Cowboy Bebop features a Creepy Child. Supposedly, whatever stopped his aging also made him bullet- and explosion-proof.
In Fate/Zero, Kiritsugu's daughter is absolutely tiny despite being eight. She's actually growing more than most homunculi of her type do but he thinks there's a 90% chance she'll stop growing before hitting puberty. In the next Grail War ten years later she's slightly older than Shirou yet is still the game's Token Loli.
The Trigun anime reinterpreted Zazie the Beast this way, apparently. Since the eternally-respawning humanoid avatar of the sand-worms' group intelligence would have been too complicated to deal with in one episode. Hell, the manga doesn't really deal with it completely.
And Kaori Yuki's Cain Saga manga series features an extremely sympathetically-presented member of the Evil Organization, Cassian, a middle-aged man in the body of a prepubescent boy, formerly employed as a knife-thrower in a circus. He joined the organization because they have weird, futuristic occult-medical hybrid technology in development which might give him some way to get an adult body. He's assigned to be the primary minion of a high-up member of the organization, Jizabel Disraeli, who's around twenty and as we get his backstory, increasingly pitiful. Dealt with well in that Cassian, even though all visual cues are against it, sees Disraeli as a kid. Cassian is fatally wounded about as soon as his pseudo-paternal attachment to Disraeli is properly developed, and Jizabel transplants his brain into the head of a fellow villain they both hate who was recently thwarted by hubris and idiocy. And the hero, in one of the hero's few success stories. He goes on the lam, and reappears as a handy plot device toward the end of the series climax. Disraeli eventually dies in his arms, lamenting the fact that he spent all this time trying to please the wrong father, Alexis, the twisted Man Behind the Man, when he should have been looking up to Cassian. Cassian has many levels in awesome.
Eriol Hiiragizawa in Cardcaptor Sakura is mostly this with a bit of Not Growing Up Sucks. He specifically chose to halt his aging, but while he looks like a child, he's mentally an adult. He doesn't have any angst over his age dissonance shown, but since he only stopped his aging so he could blend in with Sakura's classmates better, it would probably make his life after the series more complicated and restricted if he can't restart his aging.

Films - Live Action

The imaginary friends in Drop Dead Fred are real and regardless of their appearance they are childlike in outlook and behavior. However, this film may be a subversion, in that when Lizzie finally grows into her own as an adult woman, Fred stops acting like a child and interacts with her as an adult—for the last few moments that she can see him.

Literature

The Trope Namer is Peter Pan, or The Boy Who Never Grew Up, which has the Lost Boys as well as Peter Pan himself.
The story Child of All Ages is about a child who regularly drinks a potion which keeps her young (it also lets her live for hundreds of years, so she isn't about to stop, even though there are many disadvantages to being a kid).
Book example no one's going to recognize: The Meq (by Steve Cash). Also a spectacular example of a non-ending.
There's a SF short story called "Start the Clock" that features this. Basically, one day everyone on Earth stops aging, and stays in whatever "state" they were at the time... little kids have it the best, in a way, because their brains stay in the "good at learning" state... and at the point in time the story's set, they've gotten the same rights as adults (they can hold jobs and live on their own and such). Anyone going through puberty got the worst deal, since it just keeps going, deforming them and giving them health problems. Infants tend to get cybernetics, and are scary and powerful.
- Although by the time the story is set treatments to allow people to continue to age have been developed.
Oskar, the protagonist of Günter Grass's novel The Tin Drum, deliberately stunts his growth at age three, by hurling himself down the stairs, so that he can avoid being part of the horrific adult world around him. He attempts to shield himself further from adult horrors by drowining them out with his titular drum. In the end, however, a blow to the head ages him instantly.
Harlan Ellison's short story "Jeffty is Five" is about a kid who is always five. Not only that, but he is also seemingly an unconscious Reality Warper; he continually gets to see new movies starring actors who've been dead for years, new episodes of radio shows that have been off the air for decades, and read new issues of comics that don't exist anymore. This leads the narrating character, who's highly nostalgic for the Good Old Days, to spend a lot of time with him... until, as usually happens in an Ellison story, it all goes horribly awry.
The Gull of "The Age of Five" trilogy by Trudi Canavan is sort of an example of this trope. Whilst his body is that of a seven or eight year old child, he has the knowledge and maturity that he has acquired over thousands of years of life (he's also the oldest of the surviving immortals, a fact which, when revealed, causes his fellow immortals to lapse into a thoughtful silence as they wonder just how old he is.)

Live Action TV

The first episode of Eerie, Indiana involves two identical twins called Bert and Ernie who never got older than twelve and had to repeat seventh grade for thirty years because their mother locked them inside age-retarding Tupperware each night. As they state in unison, "It's a living hell". The main character pops their Tupperware open at the end of the episode, and they in turn do it to their mother, who used the same trick to stay youthful; the next morning, the twins are happily in their forties, and their mother is now an old woman.

Video Games

The Kokiri from The Legend of Zelda are given life by the Great Deku Tree and automatically stop aging at around 10.
- But as seen in Wind Waker, they can have their form changed by the Deku Tree in order to protect them (in this case, the great flood) so the tree may have given them this attribute.
Seere from Drakengard. It is more apparent in the sequel which takes place eighteen years later.
Xenosaga: Rubedo, who's an artificially created human with the power to slow down cellular growth, stopped his own aging at around age 12 (the game mentions why but it's escaped my mind). This means while he's technically older than Guignan, he presents himself as Guignan's son, Guignan Jr. or just plain Jr.
Breath of Fire IV has an entire town of these; the town of Chek is entirely populated by what appear to be kids but are actually people in their teens on up to elderly people. It's also a town entirely populated by summoners and shamans, and it's outright stated in the game that it's their proximity to the summoning temple for the gods in that universe that keeps them young.

Web Comics

Philippe from Achewood also seems like he will always be five, especially if this strip is canon...

Western Animation

The imaginary friends from Foster's Home for Imaginary Friends are real, and childlike, but never grow up, which becomes tragic when their creators grow out of them and eventually abandon them.

Real Life

Brooke Greenberg, who has a mysterious medical condition that has caused her mind and body to remain in infancy for 17 years and counting (with some anomalies, such as her bone age being around that of a ten-year-old). There's no obvious supernatural involvement, although her first five years or so of life were full of medical catastrophes that spontaneously resolved without leaving any damage (for example, a brain tumor that spontaneously disappeared).
- Though given that her telomeres^{[dead link]} are shorter than a normal child her age, Brooke may actually age faster than normal - even though she doesn't grow up.