The tendency of immortals in fantasy and science fiction to not act significantly older than they look — even if they're Really 700 Years Old.
Fair enough when you're talking about an alien species or fantasy race with a very long lifespan. Ancient vampires who behave like teenagers — or even like ordinary adults — may present more of a strain on credibility, relative to the seriousness of the genre in which they appear.
Often justified in the sense that an immortal wouldn't have to deal with many of the psychological aspects of growing older. Their bodies don't break down with age, so they don't have to come to terms with decreased mobility or mental capacity. They won't die of natural causes, so they don't have to contemplate the inevitability of death, or the possibility of an eternal reward (or punishment) and all the moral responsibility that might carry. They don't have to worry about their legacy or leaving anything unfinished, because there really is always tomorrow. They don't take on the responsibilities of parenthood, because the species survives without the need for each member of the population to produce and care for its replacements. Because of all this, these characters never need to "grow up" in the sense that a mortal does.
A darker take of this would be where the immaturity is a facade, and the character does indeed have inner angsts and turmoils that most mortals actually wouldn't be able to relate to. For example, being immortal but having mortal friends would mean watching them age and eventually perish while you remain unchanged, and while you wouldn't have to wonder about what awaits you in the afterlife, the question of what will happen to you when the world ends and there are no more people remains. Thus, inner angst is generated over stuff that mortals don't have to worry about, but is kept hidden except for special circumstances when the immortal character gets the spotlight, when such issues are thrown into light for for Hidden Depths or Character Development.
There is an argument to be made that absent changes to the body, the rate of 'change' to the mind slows even in real life; that is, the changes between birth and age 10 are vastly bigger than the changes from 10 to 20, which in turn are much larger than the difference between 20 and 40 or even 20 and 60. This argument would have it that absent the bodily changes of old age, the changes from 50 to 500 might not be so extensive as one would otherwise expect. It's also probable that a being with a longer lifespan could take a proportionately longer time to reach emotional maturity. A 100- or even 1000-year old immortal alien might be the equivalent of a human ten-year-old, while for immortal children who find Not Growing Up Sucks (or rocks) it may well be that having their clock stopped at a certain age also froze their cognitive development. They may get smarter, but not wiser.
Another part of this trope is that very often the apparent ages of immortals correspond to their status, so that the leaders are in their 30s with teenaged followers, even when their apparent age should have no relationship to their true age.
Compare the Great Gazoo, an immature Reality Warper (who thinks it really is a toy).
If The Mind Is a Plaything of the Body, then this trope may result as a consequence. See Emotional Maturity Is Physical Maturity for the broader concept of physical age being more important than actual age as regards emotions.
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Anime and Manga
Chibiusa, a.k.a. Sailor Chibi-Moon, from Sailor Moon looks and behaves like a five-year old. According to the manga, she's about 900. She still seems to find primary school to be challenging.
The Wolkenritter from Lyrical Nanoha. Vita looks like a child, and acts like a child — though it could be fairly said that she's just immature, which is a problem that doesn't automatically go away with age. Her rather sucky role in life up to that point, and during the second season, probably also contributed to her lack of control via lots of emotional pain. Still, it's awfully coincidental that the most child-like Knight in appearance would be the most childish in behavior, given that they're all supposed to be the same age.
Chizuru of Kanokon. On the one hand, she is a fox spirit, with all the instincts that entails, but on the other, she's four hundred years old, so you'd think she'd know that trying to rape a shota is bad manners. Her mom is a little better but still has entirely too much fun with said shota herself.
The Twelve Kingdoms: There are immortal characters who are over a hundred years old, but still act and consider themselves as teenagers.
Evangeline of Mahou Sensei Negima! likes to act refined (difficult when she has to look up at the person), but sometimes lapses into childish whimpering (usually when she trips and falls). Whenever she starts to avert this and act her age, Chachamaru usually tells her "please don't start pretending you're old". She lampshades this on at least one occasion, laughing ruefully about how her pre-pubescent form influences her self-perception and personality.
It's implied that Albireo "Colonel Sanders" Imma is much older than he appears. He spends a good chunk of his post-Tournament Arc appearance making fun of Evangeline. Especially her middle name.
Hinako Ninomiya of Ranma ½ is somewhere in her mid-to-late twenties; however, thanks to Happosai, her body ages incredibly slowly, so she currently looks like a ten year-old girl. She can only grow up to reflect her true age by absorbing the Battle Aura of highly-combative people around her, and even then, only temporarily. How she acts depends entirely on how she looks — she could be watching Doraemon, reading Shōjo (Demographic) or gushing over the giant panda in the living room as a child one second, only to suck out Ranma's ki and try to hook up with Akane's father as a grown, mature woman the next.
Don't forget Happosai, whose general outlook on life can be summarized roughly as "five year old child with the hormones of a stereotypical boy just hitting puberty".
In Mermaid's Scar, a subversion occurs when an immortal who has lived for 800 years as an 8 year-old boy only acts as a child to keep up appearances; his mind is anything but childish.
Some of the Soul Reapers from Bleach, particularly Rukia and Renji, alternate between acting like the teenagers they appear to be and the Really 700 Years Old warriors they actually are.
Yachiru embodies this trope, since she usually acts as the seven year old she appears to be, and only rarely shows her maturity.
Pretty much every nation-tan in Axis Powers Hetalia. Most of the characters have a "human age" of around early teens to late twenties, but being anthromorphizations of nations they are all hundreds or thousands of years old. They usually act more like their human ages (and sometimes even younger). Taken to the extreme with the bubbly and youthful China, listed with a Human age of 4000 and immortal.
In Fullmetal Alchemist, Greed has a habit of referring to older humans in a disrespectful way ("old fart", "pops", and the like), which fits this persona/appearance as a punk in his early twenties. However, it's kind of odd when he's closer to three hundred years old.
Kyo Kara Maoh's Wolfram von Bielfield is eighty-four, and he behaves like a particularly bratty and childish fifteen.
Cheri, Anassina, Stoffel, and to a certain extent Gunter and even Hube show symptoms of this. Gwendal on the other hand seems to have been an old man by sixty.
The main devils of The World God Only Knows. Elsie's about 300 and behaves like a ditzy 12 year old. Her classmate Haqua is a little better - but only a little, being about as emotionally mature as a human teen. It's a reliable source of humor in the scenes focusing on them.
Mina Tepes from Dance in the Vampire Bund seems to suffer from this intermittently. It is never made clear how much is an intentional put on, how much is her relaxing when not obliged to put up a strong front, and how much is neither; but there are times it is hard to remember that she is older than fifteen... and othertimes when it is hard to mistake her (despite her height and figure) for anything younger than fifty.
Holo from Spice and Wolf looks and usually acts like a girl in her teens despite being a harvest god hundreds of years old.
Firo tries to avert this in later volumes of Baccano!!, as getting mistaken for a fifteen-year-old is just as annoying at ninety as it is at nineteen. He is spectacularly bad at it, however - he still talks to his wife of twenty years like a boy asking out his first crush.
Somewhat back and forth in Fables. Most of the characters act like the thirty-somethings they are physically, except for Pinocchio, who, much to his annoyance, is still pre-pubescent. (Though for some reason the artist is fond of drawing him with a rather strong jaw.)
One of the subplots in the latter part of Preacher is the general immaturity of the vampire Cassidy, and its destructive impact on not just himself but the people he comes into contact with.
Topher, the vampire foe of the Runaways, is an aversion. He hasn't aged past being a teenager in 100 years. Hasn't stopped him from making a killing on the stock markets in the 1920s and losing it all in the Dot Com bubble.
All of the Endless in The Sandman display this to a greater or lesser extent: Delirium is eternally childlike, and even dignified Dream has his moments of angsting like a lovelorn teenager. On the other hand, Death looks and talks like a teenage Perky Goth, but she is also one of the most mature and philosophical characters in the series and clearly knows the weight of her age and responsibility. Later issues imply that Death matured to become the quasi-teenage Perky Goth we all know and love: in her "youth," billions and billions of years ago, she was cold and cruel.
In Terry Jones's film Erik the Viking the Norse gods are petulant children who don't care about mortals.
Let the Right One In features Eli, a vampire who has been twelve for 'a very long time'...but still acts pretty much exactly like a twelve year old. It is widely debated among fans, however, just how much her immaturity is the real Eli and how much is an act put on for the sake of getting a new Renfield.
Lampshaded in Ken Mac Leod's novel Newton's Wake: A rejuvenated woman says people like her just get a bit "cannier", and passes the rest of it off as fatigue poisons and neural decay.
Peter Pan is all about this, his skills with a blade on par with those of Captain Hook notwithstanding. Justified in his case, since his overwhelming desire to be immature is why he became immortal in the first place.
In Dragonlance, Paladine, the god of good, when in his avatar form is rather a comic figure. Some of that might be Obfuscating Stupidity but it is implied that some of it is also his real character.
Paladine's more Eccentric Mentor than anything. He may act eccentric and amusing, but even as Fizban he's always on top of what's going on.
In Harry Turtledove's Fox series, the gods are Spoiled Brats because, being nearly all-powerful, no one can discipline them. The only exception is the All-Seeing Ikos, and even he can be manipulated by his pride.
The gods of David Eddings' The Elenium and to a significantly lesser extent Dweia from The Redemption of Althalus are prone to some rather immature emotionalism. It's explicitly explained by the world-weary Sparhawk and the worldly con man Althalus in both cases as almost stemming from their immortal nature; having never needing to fear death or be chastised they don't develop maturity as well in some aspects of their personality.
Curiously, the least immature Styric deity in Sparhawk's world seems to be Aphrael, the Child Goddess. One of her brothers, Setras, appears more concerned with sunrise artwork than with humans and has to have every plan explained to him in words of one syllablebit that words are made out of.
Edward and his siblings from Twilight. With the exception of some very adult takes on death and sex, they all act like the teenagers they look like. It's explained in the books that this is a result of becoming a vampire; the ex-human is frozen in time both physically and mentally. Doesn't explain why Bella thinks that Edward is oh-so-mature though.
A more frightening take on this is the immortal children: a child who becomes a vampire will never be able to gain the self-control of an adult vampire, and will instinctively slaughter everything instead. Combine that with super-vampire strength, speed, etc. and the supernatural ability to make anyone who lays eyes on them fall obsessively in love and fight to the death to protect them, and it's no wonder it's illegal to bite children.
"You call yourself some kind of goddess and you know nothing, madam, nothing. What don't die can't live. What don't live can't change. What don't change can't learn. The smallest creature that dies in the grass knows more than you. You're right. I'm older. You've lived longer than me but I'm older'n you. And better than you. And, madam, that ain't hard."
Discworld's gods tend to be rather lacking in maturity as well as brains. (Thinking is what worshipers are for.) Small gods, who haven't attracted any followers, are even moreso: a pinch of ego and some willpower.
Avoided at first with Eli, a vampire who's been twelve for a long time in Let the Right One In. She doesn't act or think like a child, but begins to (possibly subconsciously) do so when she starts hanging around with the main character.
In The Legends of Ethshar novels, eternal youth spells freeze someone at that point in their maturity, and immortal wizards who revert themselves back to youth note that a younger body makes them act differently (especially as regards the libido.) One immortal who's been 15 for 200 years is eventually dumped by her 16-year-old beau as being too young (emotionally speaking) for him.
It's specifically noted that her emotional immaturity results from her miscasting the eternal youth spell: essentially, she's cursed to never grow up. Other eternally young wizards behave more like an old person in a young body.
Nearly every freaking god in Everworld is basically a five year old in terms of maturity and level of trust. This is a combination of naivete, an inability to change, and a lack of survival instinct. Some of the few exceptions include Loki, Huitzilopochtli, Athena, and Ka Anor, the God Eater.
The fey in Wicked Lovely. They are immortal, or at least Really 700 Years Old, but they very rarely act or look anything more than early-twenties. Probably the best example is Keenan, who is a 900 hundred year old teenager in pretty much all respects.
Honor Harrington occasionally addresses the implications of slowing the aging process and how much of your personality is influenced by hormone levels based on your age. Puberty and its associated mood swings has years added on to it.
The Dresden Files has the Winter Lady Maeve. She is easily hundreds. She has a body that can attract most anyone she wants. She is also one to throw temper tantrums when things don't go her way. In Cold Days it is implied this is not just because of Maeve's age but the Mantle of the Winter Lady which she gave into years ago. Should another woman take it from her and give into the power, in ten to twenty years she wouldn't be that different from Maeve.
The original Dracula, a vampire hundreds of years old, is a bit complicated in this respect. As explained by Professor Van Helsing: "Well, in him the brain powers survived the physical death. Though it would seem that memory was not all complete. In some faculties of mind he has been, and is, only a child. But he is growing, and some things that were childish at the first are now of man's stature. He is experimenting, and doing it well."
In The Picture of Dorian Gray Dorian's painting ages for him and takes the cosmetic consequences of his sins, which causes him to commit hideous crimes without consequences to him.
Live Action TV
The Doctor of Doctor Who, who stole a (admittedly outdated) hyper-advanced time machine and left the most advanced civilization in the universe so that he could go sightseeing, and in general shuns any sort of responsibility. Special mention goes to Four, who provides the page quote and ran around munching on candy, and Eleven, who is obsessed with looking cool and gleefully proclaims that he's a madman with a box. Even One got in on the act, starting out acting like a spoiled teenager.
Angel: "You know, I started it. The whole "having a soul". Before it was all the cool new thing." Buffy: "Oh, my God. Are you twelve?"
Anya was also something of an interesting case. Her behavior was explainable at first due to her life as a demon that had no relationship with humans. When it was eventually revealed that she was a human at one point in time, however, the explanation was retconned simply by demonstrating that she was always just plain weird. Spending eleven hundred years as a demon probably did not help.
Spike, a vampire over a hundred and forty years old, mopes like a teenager when Drusilla breaks up with him. He gets some motherly advice from Joyce Summers, a human woman a fraction of his age. (The fraction in this case being 'less than a third but more than a quarter'.) Unlike his polar opposite, Angel, his flashbacks to the past usually involve a bonfire, mod clothing, or a disco.
Angel: Wait a minute.... I wasn't in Italy in the fifties! Spike: Oh, right. Guess you weren't. (beat) Really missed out.
Buffy's original college roommate, Kathy. She acts like a typical college freshman, but it turns out she's a demon and thousands of years old. (She's also in big trouble from her guardian.)
Kathy:(whines) I'm 3000 years old! When are you going to stop treating me like I'm 900?!
The teenage vampire on Moonlight in the episode "Arrested Development". He was 200 years old and acted like an angsty teenager. It was blamed on permanent hormones, but the writers seem to have forgotten that 200 years ago, someone his age could get married and would be treated as, and act as, an adult member of society.
Trelane, in the Star Trek: The Original Series "The Squire Of Gothos", is an extremely powerful near-god and hundreds if not thousands of years old, but acted like a child...and by the standards of his race, he was—his parents showed up at the end to drag their whining kid home.
Q from the Star Trek: The Next Generation started off this way: looks to be 30, huge ego, power to match. He intentionally introduced the Federation to the Borg and put "Humanity on trial" just to make things interesting and test to see that Humanity had what it takes to be allowed to even exist. This childish behavior went on for a few seasons before the other members of the Q continuum punished him for the above mentioned reasons by taking away his powers and temporarily leaving him as a mortal. This lead to some Character Development in Star Trek: Voyager. He still liked to show up unexpectedly and sometimes pull off the occasional harmless prank, but there were bigger problems going on in the Q continuum that forces him to be more mature.
Jadzia Dax, though not technically immortal, has several lifetimes of experience. Yet you wouldn't know it if they hadn't told you about it. It doesn't help that the Dax symbiote's host from before Jadzia was a Dirty Old Man, and that the lifetime of experiences of previous hosts directly affects the personality of it's current host, with the previous host being the most influential.
Rebekah from The Vampire Diaries is a 1000 year old vampire who's interested in cheerleading, boys, and the prom. Curiously, her brothers (except for Kol) actually do act their age, leading to some fans to ponder whether a double standard is at work.
Few of the vampires in True Blood show signs of having lived for centuries and through previous ages of history. Many of them are surprisingly immature. This is particularly played for laughs with the Queen of Louisiana, who spends most of her time forcing her minions to play children's board games with her. Bill, one of the younger vampires, is one of the few who actually displays antiquated speech and mannerisms.
An episode of Being Human features Adam, who was turned into a vampire as a teenager and fed blood by his parents until they died when he's technically in his mid-40s. He behaves VERY much like a bratty teenager, largely because his parents kept treating him like a child his whole life. When he's forced to grow up a bit after their deaths, he does manage to mature pretty quickly.
Mason and Daisy on Dead Like Me both died in their twenties decades ago. Daisy is still insecure and moody most of the time, and Mason is still seriously immature even for someone in his twenties. Roxy, who hasn't been dead as long, acts significantly more mature, and George, who died as a teenager and is still roughly a teenager by the end of the series, does enough growing up that she often seems to be above Mason and Daisy's juvenile behavior.
Subverted in Highlander. While some Immortals act childish at times and some of them look quite young, they would not survive for long if they weren't willing to kill or be killed.
One Immortal kid uses other peoples' expectation that he is innocent and nonthreatening to get them to lower their guard.
The gods in many religions seem to be rather immature.
Sometimes this is a case of giving educational tales, using gods as examples, rather than making the gods outright immature - Hinduism is filled with stories like this for example, despite that in their canon gods are too great to even directly interact with the mortal world.
The ancient Greek gods are constantly interested in the affairs of mortals; they also breed with mortals. They don't seem to learn anything from experience, as far as wisdom is concerned. They are petty, cruel and constantly fighting amongst each other.
The train of events that led to the Trojan War began with Eris getting pissed over not being invited to a wedding. The modern day religion of Discordianism uses this tale as its jumping-off point.
Vampires in White Wolf's Vampire: The Requiem and Vampire: The Masquerade canonically tend to be "frozen" at where they were when they first became Vampires. They do become more knowledgeable and powerful, but they often keep the same prejudices and emotional maturity they had from when they were still alive. Therefore, even though a vampire may be 200 years old, he could still act like a hot-tempered 17 year old. Functionally, this trope pops up a lot due to the simple fact that a bunch of mortal players are dictating the characters' every action on the fly.
Subverted in the Ravenloft supplement Van Richten's Guide To Vampires, which proposes that vampires go through a psychological maturation-process which commences when they become undead, and is entirely independent of their mortal age. An octogenarian who becomes a vampire can regress to teenage-brat behavior, while a child-vampire who's (un)lived long enough can become a sober, calculating Chessmaster.
The 3.5 edition D&D supplement Libris Mortis has this as one of the cons of becoming a lich. While a lich has an eternity to learn, they can't change. They'll always have the same mindset and beliefs they did when they transformed.
For changelings in Changeling The Dreaming this trope is essential if they want to keep their Fae side intact. Though changelings tend to age much more slowly than other humans, eventually Banality will weigh heavily on their Fae souls and they become Undone. They constantly struggle to resist the pressures of growing up to hold on to their magic and immortality for as long as they can. Changelings are basically humans who have been given an Immortal Fae soul that may have been a powerful being in of itself and is merely body-hopping to survive. The humans they inhabit tend to be quite young. So it is possible, and quite common, to have a millennium old legendary dragon-slayer, a highly respected duke of the Seelie Court, or a highly valued scholar of ancient lore sitting in a living room playing with toy trains until mommy calls him for bedtime.
Xenogears features several characters who are quasi-immortal. Some have lived for hundreds of years, a few for as many as ten thousand. Emperor Cain and the Gazel Ministry act as one might imagine. The former is a world-weary, very old man who has kept his moral compass intact due to guilt over a sin committed long ago, the latter being very anxious to transcend to a higher level of existence and possessing of no moral compass whatsoever. Then, there is Miang, who has lived as long, but in a different manner: she possesses a new body when her current one dies. When we meet her, she has the body of a beautiful young woman and appears to act like one, being flirtatious and sexually-active. Yet, it's difficult to tell how genuine this is, because her entire existence is devoted to executing the mother of all plans, and everything she does serves this end.
Many Touhou characters, though it might be side-effect of how most characters are immature and most are Really 700 Years Old, with predictably frequent overlap.
The Scarlet sisters are the most obvious example, as they gained immortality by forgoing maturity, with Word Of God stating that "creatures of [Remilia's] kind forfeit their growth and maturity in exchange for eternal life. In other words, she can live forever because she never grows up." Thus, they have the appearance and mentality of ten-year-old children. Remilia at least has the experience to act mature and can get serious if required, but Flandre doesn't even have that, what with spending 500 years in their mansion's basement.
Kaguya Houraisan kept up a centuries-long war with Mokou where they killed each other daily (for Mokou it was one part revenge, two parts something to pass the time), and treats her servants like playthings for her amusement. How Eirin (an actually mature immortal) puts up with her is anyone's guess.
All fairies are excellent examples of this trope. Justified due to The Fog of Ages.
Subverted with Suwako Moriya. Despite having the appearance and mannerisms of a little girl, there are a lot of indications that her childish behaviour is largely an act and that she's a good deal more intelligent than she lets on. She is, after all, a goddess who has existed since ancient times.
This is Tenshi Hinanawi's problem. Most Celestials achieve their status through diligence and careful introspection in their lives, as well as the ability to fight back against Shinigami; her clan was quickly whisked up to the heavens by a kami for good work maintaining geologic keystones.
Mother 3 has Porky. He will stay that way forever due to both time warping too many times and for trapping himself in the Absolutely Safe Capsule at the end of the game.
The angels and demons in the Disgaea series are all over a thousand years old, but since time flows differently in their dimensions, they age 100 times slower then normal and act exactly as old as they look.
All of the four goddesses of Neptunia exhibit this trope, one way or another.
Joshua from The World Ends with You. Fantastic godlike powers, but he spends his days loitering around Shibuya trolling Neku. It's assumed that he was a troll in life, and immortality hasn't caused him to grow out of it, despite his job's responsibilities. Hanekoma might count as well, though his age is never given.
In Fire Emblem Awakening, Tiki is the much revered and millennia old Voice of the Divine Dragon, who normally acts wise and aloof, but her profile explicitely mentions that she also has a more childish side. Say'ri experiences this firsthand when Tiki first Blows A Raspberry at her and then tries to stuff her mouth with an apple in their B support.
From the same game, Nowi is a Manakete just like Tiki and is more than thousand years old, but has the looks and mindset of a young girl. Supports reveal that this is at least partly a case of Obfuscating Stupidity, however.
Fate/stay night: Saber is, we are told, not actually fifteen; after receiving her sword and becoming King Arthur, she didn't age over the next ten years, and she's really in her twenties. Not only does nobody mention how strange it is for her to have a romance with the seventeen year old main character, but she's as naive emotionally as a real seventeen year old, which is Hand Waved by claiming that as the king she had no personal life.
Arcueid Brunestud, of the visual novel Tsukihime, is also much like the previous entries. She's an ancient True Ancestor, but she was bred to be a weapon and not a person by her own race, and so they kept her asleep all the time except when she was sent to kill someone... so her demeanour on the outside world is not unlike that of a curious and confident child, marveling at everything new she comes across and being generally naive and emotionally outspoken. She reallyisn'tany older emotionally than she acts.
Ciel from Tsukihime has a similar situation to Saber's going on, but in that case it's actually lampshaded in Kagetsu Tohya.
Rika from Higurashi no Naku Koro ni, despite being Really 700 Years Old, her outward behavior and speech patterns are still those of an adorable, cheerful girl. As it turns out though, this is only an act so as not to alarm everyone who's oblivious to Hinamizawa's dark secret. Mentally, she's a rather serious adult. That said, she hasn't grown nearly as old mentally as she thinks she has.
Played straight with Hanyuu, a.k.a Oyashiro-sama, who's even older, but is really quite shy and easily flustered. She can be quite serious and mature though; the manga tends to make her overly mature, and the anime tends to make her too immature.
Beatrice is perfectly capable of being the dignified and elegant witch that she claims to be, but is often very childish and mischievious. This is because she's not actually a thousand years old like she claims. She's actually 19 years old.
Lambdadelta is supposedly a great witch herself, but usually comes across as something of a ditz who's obsessed with fellow witch Bernkastel. Another subversion, since her childish behaviour is really just an act.
Bernkastel appears to avert this, being rather cold and emotionless, though this is also subverted since she's not as emotionless as she seems, and as her displeasure at losing shows more as time goes on, she actually seems to show more immaturity.
El Goonish Shive takes the effort to make it a Justified Trope as the immortals erase their own memories to avoid the complete boredom involved in knowing everything.
Played straight with Chaos, the immortal who refused to "die" (the erasing memories thing) with the attention span of a gnat who manifests as a Creepy Child. The immortal who explained the whole thing mentioned that they get "more powerful and less sane" as time passes.
The angels Rumisiel, Cassiel, and Vashiel from Misfile range from 437 years old to possibly several thousand years old and yet still act like teenagers. Vashiel is somewhat more believable, just deeply honest (to the level that it's physically impossible for him to lie) and highly clueless about stuff he hasn't paid much attention to in his long history of smiting.
Xykon is not particularly mature for an immortal lich with more than a century of life behind him. Start of Darkness reveals that he was never very mature to begin with, even as an eighty-year old man. He even lampshades how, even at his advanced age, his "life's wisdom" boils down to little more than "sure, being a badass villain is a barrel of laughs, but what's the point if you can't even enjoy the little things in life" (which to him is mostly watching people die gruesomely and drinking coffee). That said, Xykon can be surprisingly clever and patient if he wants to.
Redcloak is another example, played in a different way. His aging processes have been retarded by the magical cloak he wears, and he's eventually called out on this by his (normally aging) younger brother: He's spent most of his time following the Dark One's directives (and later, Xykon's) and hasn't used any of that time to actually live a life; and because he never ages, he hasn't been forced to move on from the tragedy of their past the way Right-Eye had to.
Mab and most of the other Fae from Dan and Mab's Furry Adventures , sort of. Essentially everything they do is a matter of "It Amused Me," but they operate and think in an entirely different way from anyone else, and evidence suggests that they can also be mature if that's what amuses them at the time. Additionally, since they're immortal and have a flexible view of time, this behavior might be a way to avoid going totally insane. There is also a somewhat sinister slant to their apparent immaturity, especially given their general view of things as being a game of sorts, and that fact that despite near-omnipotence they will still allow their friends to die in preventable ways.
This behavior also appears in some of the mortal-but-extremely-long-lived characters. Abel and Kria don't always act like they are in their 400's. Dan and Regina have some excuse though since they actually are in their 20's.
Incubi and succubi in general are creatures of emotion, and apparently have a harder time controlling their own in turn, though the clan leaders are more than capable of being serious - perhaps because they are millenia old. Demons have no such excuses, however.
From Homestuck, even though some of the pre-scratch ancestors have existed for so long time has lost all meaning for them, they all still act just like awkward, silly, hormonal teenagers. This may be because they're dead and thus removed from the mechanisms that cause change in life. Sanity Slippage, or at least Took a Level in Jerkass, is also implied for most.
Her Imperious Condescension is a galactic conqueror who is at least several hundred years old yet the few times she speaks she uses either ghetto speak or pink sparkly text.
Futurama parodied this trope in the episode "Where No Fan Has Gone Before": it turns out that Melllvar the "immortal" energy being is only 34.
Played for laughs in the opposite direction though - when Melllvar's mother drags him off to dinner and Fry makes a Star-Trekky comment about how they thought he was a mighty, god-like being, but he was only a child (see Trelane, above). Then his mother says, "Child? He's thirty-four," playing up the Basement-Dweller trope.
Demona is this all the way. Macbeth doesn't suffer from the same problem, despite having received their immortality in the same way, likely because even when Demona was an old woman she was still an immature punk, while Macbeth was fairly mature as a young man.
The Children of Oberon frequently do act like children: immature, god-like, arrogant children. As Greg Weisman said, they have "Great power. Little or no responsibility", in addition to being immortal, and apparently never needing to worry about disease or even feed themselves. They get to spend their whole lives playing games and fighting each other. They aren't necessarily evil, but even the best of them don't actually grasp concepts like mortality.
Ironically, the series implies many of them were once worse. Oberon leveled a thousand and one year exile to force them to grow up. It worked on a few of them.
In Fosters Home For Imaginary Friends, the imaginary friends don't age, either mentally or physically. Since they were made to be childhood companions, they're almost all intrinsically child-like.
Takua, one of the oldest beings in BIONICLE, likes to put light crystals on his head and run around pretending to be a bunny rabbit.