The characters from Ah! My Goddess have been college age for nearly 23 years now. Their surroundings keep getting adjusted to match the times. Even though Skuld has remained a kid for that whole time (except that one time), she doesn't count.
In Arabian Nights: Adventures of Sinbad, the main character never seems to age, despite the fact that his adventures could easily take months or even years.
In the anime version of Ascendance of a Bookworm, the main character is stated to be seven when the series starts, and when she finally makes her first book she says that it's been two years since she started trying. Neither she nor any of the other child characters have changed at all in appearance in that time.
The original Astro Boy had this in spades. Though the title character is a robot and is thus justified in not growing up over the course of several decades, his human classmates have no such excuse. What makes this especially odd, is that Astro's "little sister" Uran, also a robot, actually did grow up! She went from being a short, chubby preschooler in her first appearance, to being able to impersonate Astro with a simple costume change, to the point where she looked more grown-up than her "big brother", as a slender young woman in the later stories, complete with artificial breasts!. Tezuka also experimented with drawing Astro looking more like the teenage adventure heroes that were popular at the time, but apparently, his readers didn't go for it. Then there's the Astro's Been Stolen story, where an attempt is made to give Astro an adult body, but it turns out to be a piece of junk that only has the same power level as his original despite being much bigger. The story ends with him musing that Growing Up Sucks and if you can avoid it you probably should.
A plot necessity in Case Closed. Being a teenager trapped in an elementary school body, if time progressed linearly, he would have regained his age the long way over the 20+ years the series has run.
Crayon Shin-chan and friends has been 5 years old since Shin-chan's 1992 debut, despite the manga and comics showing the characters celebrating Christmas, Coming of Age Day, and at least one volume (published in late 2002) showing the Nohara family anticipating the upcoming 2003 New Year countdown (acknowledging that yes, time does flow in their universe and they're not forever frozen in the early 90s).
All the main cast of Doraemon have remained at 10 years of age in their "current" timeline ever since their 1969 debuts, despite some episodes showing them grown-up in the future.
While Dragon Ball is notably renowned for averting this trope (and pioneering its aversion in other series), it comes into play in Dragon Ball Super with the various kid characters. According to the timeline placement, Goten and Trunks should be in their mid-teens by the second arc and older later,note Pan is said to be four years old at the end of the series, which is set ten years after the Buu arc, and she's at least a few months as of Resurrection F. Thus that movie/arc takes place six years after Buu. Goten and Trunks were respectively 7 and 8 during the Buu arc, so by Resurrection F they'd be 13 and 14. Six more arcs have passed since then (Champa arc, Zamasu arc, Universal Survival arc, Broly arc/movie, Moro arc, and Granola arc), and their designs haven't changed. but still look and act as they did in the Buu Saga of Dragon Ball Z. Krillin's daughter Marron, while a more minor character is an even more egregious example, still looking and acting like a toddler despite being around ten years old at this point.
None of the characters in Kocchimuite! Miiko has aged despite the serialization in Ciao magazine has been running since 1995. Eventually averted in the 29th volume promoting the main cast to sixth grade, although it takes five volumes to show them graduating.
The characters in Kochikame never age when the present date moves along with real life and the manga being a Long Runner status of over 30 years. Many of Kankichi Ryotsu's flashbacks take place 30 years in the past depicting 1950s Tokyo. One exception is Daijiro Ohara's grandson who is the only character appear to age who started as a toddler now around 10 years old.
Minami-ke is a prime example. It's not really noticeable in the manga but for those following the anime, this is especially glaring. For example, at least three New Year's celebrations have been shown... and yet no one has advanced a single year in each of their respective grades.
Mitsudomoe will always be in the sixth grade, no matter how long it runs. Which is why so many Christmases have passed.
Ojarumaru has been running for over two decades, and yet Ojarumaru and the other characters do not look like they have aged at all.
Ouran High School Host Club lampshades this; the manga's narration politely asks the reader to ignore the fact that, despite various seasonal changes, no one has gone up a grade. This practice ends in chapter 72, in which Honey and Mori actually do graduate (as do Nekozawa and Kasanoda), though they promise to stop by every now and then. It comes as quite a shock to Haruhi, and signals a turn towards some slightly more serious and dramatic storytelling for the remainder of the manga.
Pretty Cure initially averted this — the first season ended with several recurring characters graduating from middle school, and the second shows Nagisa and Honoka dealing with the new stresses from becoming upperclassmen. Then the series entered Comic-Book Time, and when Nagisa and Honoka returned for the Crisis Crossover after being offscreen for three years, they were still the same age. They try to avert this for some of the Distant Finales in the later seasons, but their continuing appearances in the All-Stars films renders it all naught since they still retained their initial ages as if nothing happened. This is what ends up making Power of Hope ~PreCure Full Bloom~ all the more surprising amongst long-standing fans, since it's the first full Pretty Cure season to break out of this trend and show the Cures all grown up, specifically the Yes! 5 and Splash Star teams... only to end up Zig-Zagging this when Nozomi re-awakening her transformation to Cure Dream de-ages her back to how she was at the end of GoGo, creating a weird hodgepodge situation where it's the actual Cure transformations itself that's not allowed to grow up.
Even though there have been at least two New Year's Eve-based stories, a slew of Christmases, and too many summer vacations to count, Ranma ½ is perpetually fixed in Ranma and Akane's first year of high school (10th grade). Made even more conspicuous since Ranma arrived in the middle of the school year, and both fashion and technology change to reflect the real world (the manga began in 1986, and ended ten years later). There was not one single birthday throughout the entire run, and Kuno, who introduced himself as "Age: 17" in volume 1, would still claim "Seventeen years of age, the epitome of manhood" as late as volume 33, published in 1994.
The anime was especially bad about this. There's been at least one time where it's mentioned that Ranma has been living with the Tendous for at least a year or two — yet he's still sixteen.
Urusei Yatsura also. Lum, Ataru, Shinobu, Mendou and the rest were 17 years old and on the cusp of high-school graduation for years on end... And how many summer vacations and Christmases did they have? Although Ataru did have one birthday during the run of both manga and TV series (the setup for a plot where he feared Lum had forgotten) which is one more than the Ranma cast got.
Sgt. Frog: Even though every season of the anime features holiday and birthday specials and there are direct references to previous years, the human characters still keep their original ages and are still in the same school years. The same happens with Tamama, who still keeps a tadpole's tail and white face, even though Taruru, a Keronian younger than him, matured in the 2nd season.
Lampshaded by the manga, when Fuyuki said that he was "just 12(?) years old" in a later volume.
Irregularly contradicted by the anime itself, which is also the biggest offender due to the number of holiday and anniversary episodes. Paul, in Episode 92, mentions that Momoka's birth was commemorated 13 years ago, and Natsumi was said to be 14 in the second movie, which means that the entire cast aged at least one year. There are also various references to the Keroro platoon spending years on Earth and vague comments about the human characters getting older. However, official guidebooks still keep everyone's starting ages and school years as the only official ones.
The newest databook for the manga (as of volume 23) actually said that the human characters had aged one year since the start of the series, breaking away from the manga's previous references to the lack of aging of the human cast.
None of the kids grow up in the gag manga Urayasu Tekkin Kazoku. The kids are always in second grade despite various seasonal changes in each volume. It takes 31 volumes until the Ganso! sequel series premiere promoting the kids to third grade. One exception is Yuta, Kotetsu's younger brother. In the early chapters, he was a diapered infant, now he's at kindergarten age.
In the YuruYuri manga, the characters actually break the fourth wall to discuss a few of the long term implications of this once they find out that their series is one of these. However, the mangaka ended the chapter by stating that they might move up a grade some day. Episode 10 of the anime's second season suggested that it's the result of being stuck in a sort of time-loop.
Yo-kai Watch has done several episodes for the same annual holidays, but Nate is perpetually a fifth grader. This was eventually averted with the Spin-OffspringYo-kai Watch: Shadowside, which stars Nate's daughter 30 years in the future. Then played straight again when the original anime was brought back after Shadowside ended, where Nate is still a fifth grader.
