The Beverly Hillbillies: Jethro Bodine, in spades. Although his emotional and mental immaturity is owed to his lack of education (he's proud to be a sixth-grade graduate) and awe at being introduced to the Beverly Hills lifestyle.
The Big Bang Theory: While all the characters indulge themselves in childish things, Sheldon insists that someone take care of him the way his mother would when he's sick (or even just homesick), locks himself in his bedroom where no one else is allowed when he's furious, curls up into a crying ball of sad on his bed when he's embarrassed, runs away from home when he's upset, is practically traumatized by the sound of people arguingnote Although this one may be perfectly justified, as his parents often got into arguments when he was a child and it is also implied that a lot of the arguments were exceedingly violent (he mentioned that his father would start throwing plates and shattering them in the kitchen, and that his mom planned to place glass shards in his father's meatloaf), even when they said to Sheldon that they stopped fighting, and is stubborn and petty beyond all reason. The only thing on this planet that can force him to behave rationally when he's angry or depressed is an order from his mother, who Lenard calls "Sheldon's Kryptonite". He also responds positively to being patronized by Penny, especially if he gets a toy robot and a comic book out of it. Lampshaded by Bernadette at one point, after she successfully got him to go to bed by first reasoning with him about the effects of lack of sleep, and then simply treating him like an overgrown child and sending him to bed.
Bonanza: Several episodes have featured characters who were mentally "slow" – some villains, some sympathetic characters, others one-off good guys the Cartwrights aim to help. One of the best-known examples was "The Ape," from the show's second season, where a large man named Arnie has traces of autism, is unable to read social cues and (more worryingly) has a fierce temper. His fierce determination to win over a barmaid that has no interest in him is what eventually leads to his downfall, despite Hoss' own determination to help focus Arnie and mentor him into a farmer.
Detective Jake Peralta is a very good detective, but he's almost incapable of acting like an adult.
Sgt. Terry Jeffords: The one mystery [Jake] can't solve... is how to act like a grown-up.
To a lesser extent, Detective Amy Santiago is a female version of this trope. Where Peralta acts like the high-school class clown who never learned maturity, Santiago gives off the impression that she's still running for high school valedictorian.
Richard Castle is this trope in spades. He sets up laser tag in his house, plays with remote-controlled helicopters and other toys, buys property on the moon, and often has to be put in line by his teenage daughter. However he is capable of acting maturely, he generally just chooses not to.
The Christmas That Almost Wasn't: Prune exhibits this, even before rediscovering his forgotten childhood. He's extremely petty in his actions and outlook, even breaking toys and blaming it on Santa so the rent money all goes to repairs.
Morgan Grimes of Chuck has strong shades of this in the first two seasons, although around the time he gets promoted to assistant manager of the store he finally begins growing up. He never completely abandons his love of video games, comic books, toys, and other such interests, but his maturity level from season 3 onward is strikingly higher compared to the beginning of the series.
The First Doctor. He sees himself as a dignified old man but his maturity level is closer to that of a fourteen-year-old, loving showing off to girls, being surly to authority figures, struggling with social skills, incredible self-centredness, gleeful meddling and boundless curiosity (not to mention his somewhat vertical relationship with Ian and Barbara and his incredibly parallel relationship with Vicki). Later canon pretty much states the 'old man' aspects of his character were actually just a childlike attempt to look important. All this said, all of his later incarnations trust him to the point of seeing him as an authority over them.
The Fourth Doctor. One of the most dignified, mature and authoritatian Doctors of all - the Third - was immediately followed by probably the most blatantly childish and anti-authoritarian of the lot. He offers everyone sweets, plays with children's toys, doodles cartoons of people he dislikes, loves playing and running around and getting attention, tends to sulk when he can't get his way, and has childish Character Tics that make him bizarrely cute despite being huge and imposing. He's sensitive and vain about his age, constantly lying about it to seem younger. He absolutely detests authority and is willing to go anywhere, do anything to avoid taking orders again.
The Eleventh Doctor plays the age card less than previous Doctors did during an argument, and seems to even forget his decrepitude at times. The War Doctor isn't amused: a senile git of a man, Eleven has retreated from his grim past into a world of childlike frivolity. This changes once he saves Gallifrey in "Day of the Doctor": He pointedly chooses to stay behind and age into an old man on Trenzalore, as if unconsciously deciding to 'grow up.'
Dollhouse has Topher Brink who, for his mid/late-20-somethingth birthday, creates a buddy to play video games and tag with him. He gets much, much more childlike post-series tragically.
The Dukes of Hazzard: James Best once said of Sheriff Rosco P. Coltrane – the character fitting this trope – that Rosco is like a 7-year-old child who loves initiating car chases. Indeed, much of Rosco's behavior is that of a 7-year-old. While that of Hazzard County Commissioner J.D. "Boss" Hogg (Rosco's boss, confidant and partner in crime ... and his brother-in-law) is similar to the 10-year-old big brother.
While everyone in Friends tend to act childish at some point, Ross is the worst one of the group. He usually resorts to petty revenge to get back at Rachel whenever they break up from their on again off again relationship (dating women just to make Rachel jealous) and gets into childish fights with his sister, Monica, such as hogging the TV or calling her childish names. For the latter, Ross thought his squabbles with Monica as they grew up together was harmless fun and that is why he kept doing it well into adulthood until Monica confessed that she hated Ross when they were kids because of his bullying.
Joey is almost as bad in this regard. He constantly mooches off Chandler (with everything from rent payments to acting classes), he refuses to maintain a steady romantic relationship even when he's well into his mid/late-30's, and he's hopelessly idealistic about his acting career despite clearly being a pretty lousy actor. As the show went on these traits were Flanderized for him, and by the final season he was buying Cabbage Patch Kids dolls, being entertained by a book intended for preschoolers, and had a written letter of his being mistaken as one written by an actual six-year-old.
On Fringe, Walter Bishop is a curious example of this. As a young man, he was a normal, mature adult. But then his partner cut pieces out of his brain and he spent 17 years in a mental institution straight out of Victorian England (okay, not quite that bad). The new Walter Bishop, while he retains his prodigious intelligence, is a Cloudcuckoolander who cannot manage the basic necessities of life on his own, and is dependent on his adult son and his FBI-agent-turned-lab-assistant to provide for his needs. While his foibles are often played for comedy, later episodes also play up the pathos of his situation; unlike most Man Children, Walter remembers having been capable of living on his own, and his humiliation and sense of loss are keenly felt.
Rory: You'd have to cut him open and count the rings.
On Good Eats, Alton helps out a 32-year-old man who has his mother come by every morning and make him breakfast, at the mother's request. He eventually learns to at least cook one meal for himself, but his mom still does his laundry for him.
iCarly: Spencer is a sculptor for a living, often making whimsical and sometimes weird sculptures that usually end up catching on fire or exploding before being perfected. He loves light-up socks, has a pet goldfish (that he often forgets to feed, resulting in another pet goldfish), and once went to law school for three days.
The most physically intimidating of the Impractical Jokers - heavy-set, scowly Q - had to don a nightshirt and tug around a teddy bear in an Ikea. Surprisingly, he managed to get a customer to tell him a bedtime story.
The IT Crowd: Moss is a man in his thirties who acts and speaks like a 4 year-old most of the time, doesn't swear, still lives with his mother and sobs uncontrollably when confronted by bullies...
Roy to a lesser extent.
Ellen May in Justified. The relationship between Delroy and Ellen May resembled that of an abusive father and child. Later, her relationship with Ava took on a similar dynamic.
Doug Heffernan from The King of Queens. Whenever he's having an argument with Carrie, he often goes to extreme lengths for petty revenge, often injuring himself or worsening the conflict. He has been shown to have a very juvenile sense of humor on several occasions, and one time fought with his father-in-law over a toy in his cereal box, just to name a few things.
Lenny and Squiggy from Laverne and Shirley are this trope. While they do have some adult ambitions like getting girlfriends and starting a talent agency, they still have the same mindset as kids and often do childish things like drinking chocolate syrup and watching cartoons.
The Law & Order: Criminal Intent episode "Cruise To Nowhere" focuses on a young (about 20 years old) poker genius named Joey Frost, who acts like a petulant child and whom Goren describes as having the emotional maturity of a ten year-old. It eventually turns out that there's a sympathetic reason for this behaviour: a horrible childhood.
Goren himself fit this trope in the early seasons. Witness, for example, his glee at discovering a synthesizer that says things like "Oh, baby!" when you hit the keys.
Sometimes in later seasons, too, such as in 'Vanishing Act' when he reacts with similar glee at the various magic trick thingies.
On Leverage Parker has shades of this given that she was somewhat emotionally stunted by becoming a thief at an extremely young age.
Jacob from LOST began as an immature, emotional man with little social skills, plus he lived with his adoptive mother for nearly thirty years. Centuries later, however, Jacob's outgrown his previous phase.
Has he though? "You've got ink on your forehead."
Stuart of Mad TV. Although the character is supposed to be an actual child, he appears as one of these because he is played by an adult man.
Radar in some seasons ofM*A*S*H. He does have some growing up to do in "Idols", and, as a final show of growing up, leaves his teddy bear behind when he goes home.
Vince in The Mighty Boosh is constantly eating sweets, writes in crayon and has an imaginary friend made out of bubble-gum called Charlie.
Mr. Bean sleeps with a teddy bear. In the first episode, he puts two dolls on the table when he sits down to take an examination. In general he is of the more common, Fish out of Water type, although his strangeness goes beyond childlike and into the realm of truly bizarre.
The Munsters: Herman Munster. He enjoys watching children's programs, and frequently throws foundation-shaking temper tantrums.
In the same series, Earl had caused his teenage babysitter to become pregnant by poking holes in the condoms she and her boyfriend were using, because he had a crush on her and he was jealous. The couple is still together, having gotten married as a result of the girl's pregnancy, and their son is now grown up. He, however, is a mess; he dropped out of school, lives in the basement, is whiny and demanding, and uses a Jar Potty so he doesn't have to come upstairs to use the bathroom. Earl decides that the way to cross "Got the babysitter pregnant" off his list is to help him grow up. It's actually Randy that ends up doing it, though.
And now they're married and live in the same house that they never clean, repair, or pay for. Ben has to babysit them.
Tom and John-Ralphio also fit. They started Entertainment 720 together so they could look cool. The business tanks into debt in about 2 months because they didn't know that companies have to make money.
Leslie fits, too. She is cheerful, hyperactive, and a little naïve. Not to mention her fondness for candy and dislike of vegetables. She is competent, however—indeed, very competent.
Shawn Spencer from Psych, especially in the episode Ghosts: Shawn responds to his mother's unexpected appearance by hiding out in his old bedroom while on the phone with Gus, a conversation during which he becomes enamored with an unopened box of Shrinky Dinks, a teen magazine in pristine condition (which he tries to read to Gus over the phone) and playing with an old Furby. The latter one is especially telling as he would have to be 21 at the youngest to have previously owned a Furby.
In one episode, after freaking out about his Nintendo DS being stolen, his girlfriend tells him to stop acting like a child and he responds "I'm not acting."
Justified, in that there was an engagement ring for said girlfriend hidden in the Nintendo DS.
It's hinted that a good deal of Shawn's childish moments was due to the strict upbringing by his police father and not having been able to make more life choices and such.
Sherlock in Sherlock. He does very, very, very strange things to solve cases, and...well, there's a lot that would qualify him for this category.
Caitlyn on Saturday Night Live for the same reasons as the above is supposed to be a 10 year old girl, but was played by then the well into her 30's Amy Poehler
In one episode of Suite Life On Deck called The Starship Tipton, George Takei played a descendant of London named 'Rome Tipton'. He is usually seen with a teddy bear and acted very much like London. He was even still in school.
When Castiel is dealing with Heavenly matters, he's a stoicBadass Longcoat. When he gets isolated among human beings, however, he descends into this at times, like when he goes to a brothel, suddenly craves meat, or...
Castiel: "I found a liquor store... and I drank it." (falls onto Sam)
Dean Winchester is this whenever the writers decide to take a break from angsting him. For example, he gets super-excited about classic monsters like a proper werewolf, and makes movie references non-stop.
In Bad Day At Black Rock, while his run of luck allows him to have incredible reflexes and aim, Dean says "I'm Batman" after taking out an assailant, and looks genuinely disappointed/hurt when Sam responds with a "Yeah right, you're Batman".
In Season 6, Dean also shows his childish excitement of classic Western movies and the opportunity to go to the good ol' West.
Neal Caffrey from White Collar shows shades of this. When Peters tells him it's wrong to have nice things you haven't earned his reaction is a childish "why not?". Also, whatever mistakes he makes always seem to because he can't keep his feelings in check.
Max from 2 Broke Girls has shades of this while she's not as immature as a child, she has a child like entusiasm for things like drugs and candy. She's essentially what Amy Phoeler's Saturday Night Live character Caitlin, a hyperactive 10 year old, may be like 15 years later. She also could possibly be a compulsive liar as many of her stories seem way too farfetched to be true and something a child would tell.
Possibly every male-lead on a family sitcom ever, from "Yes, Dear" to "Still Standing".