In Real Life, adults furthering their education by returning to school is a fairly common occurrence—and one that can happen for any number of reasons, even out of a genuine love of learning.
However, in the realm of movies and TV, this situation is looked upon as purely humorous. Plots in which the main adult character—and it usually isthe lead; only occasionally will you see a more minor character as the focus of this sort of story—has to return to school are pretty much exclusive to the comedy genre.
Your average John Q. Dropout's reason for completing his education is nearly always related to his career, sometimes to obtain a new job requiring a higher degree of education and other times because his current job demands it. Stupidity and incompetence will often be lampshaded. The character will often be thrown amongst people outside their age group, or at least act in that way.
When actual school children have to repeat a grade you want Held Back In School.
If you're looking for the 1986 comedy of the same name, go here.
The title character of Billy Madison had to retake all 12 grades in order to take over his father's company.
In An Extremely Goofy Movie, Goofy had to return to college (and the same one his son, Max, was attending, no less!) to get a job.
Goof Troop actually had one where he had to repeat grade school.
The premise of the movie Back to School is that Rodney Dangerfield's character goes to college in order to convince his son that it's worthwhile (after the son uses the father's self-made success as an argument that college isn't necessary).
The title character in Ernest Goes To School has to redo 12th grade to keep his job since the school board require all school employees to have a high school diploma.
Nick Rivers from Top Secret appears to be back to school, painfully, in the middle of the movie. He is tremendously relieved when he realizes he was only being tortured by two goons and that was just a nightmare he had when he passed out.
Larry Crowne is a fairly realistic version: Larry went into the Navy right out of college and only goes when he get's fired from his job for not having a college diploma, so he goes to Community College to have a better chance on the job market.
In the Don Camillo e Peppone series, there is one arc where Peppone (the mayor of the village) has to take the primary school finals because he missed them during the troubled years of WW 2. He almost fails; Don Camillo trades the correct solutions for political concessions.
Done in an episode of Friends where Phoebe wants to do a literature course, but has it ruined by Rachel who doesn't take it seriously. For a moment it looks like they'll subvert it by having Phoebe give a genuinely impassioned explanation of how she never got to go to high-school and genuinely wanted to learn something, only to go straight back to comedy by having neurotic control-freak overachiever Monica accompany her next-time.
Judge Stone on Night Court was found not to have completed his education.
The central premise of Strangers with Candy: Jerri Blank dropped out of high school and became "a boozer, a user and a loser", but decides to clean up her act and go back to school - aged 46.
"If I don't graduate by the time I'm fifty, I'll be the laughingstock of Flatpoint High!"
On Full House, in episode 6 of season 6, D.J. and Kimmy request Joey and Jesse's help with a "Stay in School" campaign, and they are stunned by Jesse's refusal to help. The entire family pressures him into telling the truth: that he is actually a high school dropout. With only one English credit missing, Jesse is inspired by his wife to take a night course and earn his degree.
In The George Lopez Show, George goes back to school after there is a PTA meeting specifically targeted at parents who didn't go to college. Max decides he doesn't need to go either so George wants to teach him a lesson. In the next episode, George drops out and tells the teacher he was in the military and got sent to Iraq. Hilarity Ensues.
In The Steve Harvey Show, Steve and the gang all have to take a required computer class, which Lovita teaches. The usually overachieving Regina fails the class miserably while slackers Steve and Ced pass. Hilarity Ensues.
On The Golden Girls, Rose goes to night school to earn her diploma as she missed most of her senior year due to a bad case of mono from manning the kissing booth at the school carnival. Dorothy is the teacher and fails Rose because she failed the history final. When Dorothy reviews the test paper with Rose, she uses some oddly applied knowledge and passes, thus earning her high school diploma.
On Mama's Family, Thelma Harper went back to school to earn her high school diploma by completing English Literature - a class she had trouble with originally because she didn't understand the material. She has trouble learning to appreciate The Scarlet Letter until her friend, Iola, describes it in the manner of a romance novel which results in Thelma reading the book and impressing her teacher.
On Married... With Children, Peg discovers that she never graduated from high school because she was one credit short (she failed Home Economics), so she enrolls in Kelly's home ec. class and the two have to prepare Jell-O and crowned rack of lamb for their final exam. Peg's project gets eaten by Al, and, in true Bundy fashion, Peg steals Kelly's Jell-O dish and turns it in as her own, thus allowing her to finally get her diploma, and forcing Kelly to go to summer school.
Peg talks Kelly into thinking she's going to have a great summer, allowing Peg to walk away. Kelly finally catches on ... many seconds later.
Jill on Home Improvement, after she got laid off from her journalistic employment. Her education lasted through the remainder of the series' run.
This was the premise of the Rhea Perlman SitcomPearl. Pearl was a mature woman from modest up-bringings. When she realized she had missed out on a lot, she decided to go back to college, in spite of her grown son's protests. She made a bunch of new, but weird, friends and was constantly in conflict with her snob philosophy professor (played by Malcolm McDowell).
The entire premise of Community is that the main character is forced to go back to college and earn his bachelor's after the government learned his was a fake. It is also revealed that Senior Chang did the same thing and will be joining the group as a student the next semester.
A subplot in Desperate Housewives involved Lynette's husband Tom going back to college after getting laid off.
This trope was the premise of the Moesha Spinoff, The Parkers. Nikki Parker (Mo'Nique) had to put off going to college because of a Teen Pregnancy and a subsequent failed marriage. She decides to go to community college, much to her daughter Kim's embarrassment because she's also attending the same school. Hilarity Ensues.
Bookman does this on Good Times. When he and wife Violet were dating, he lies and tells her that he was in college, when in reality he never finished high school. After much Hilarity Ensues and a Not What It Looks Like, he finally tells her the truth and says that he was inspired to go back to school because he saw Jesse Jackson on TV encouraging Black people to get an education and be positive members of their community.
In another episode, Florida (who dropped out in the 11th grade) employs this trope because she wanted to set an example for the children as well as have an accomplishment outside of being a wife and mother. James (who dropped out in the 6th grade) forbids her from going to school because he was insecure about having a wife who was more educated than him. Florida drops out, preferring to keep peace in the home. In the end, the kids and Willona convince James to allow Florida to resume her studies, with James deciding to enroll as well.
Jimmy takes an elementary school science class in Yes Dear after realizing he's not capable of helping Dominic with his homework. Christine also goes back to college during the series, and, in one episode, joins a sorority.
In the DVD Commentary, Smith says he liked the idea of sending Jay and Silent bob back to High School and the only reason why he hasn't done it is the royalties he'd have to pay the Degrassi people.
In one episode of Boy Meets World Amy enrolls in a creative writing class at the local university after realizing she's bored with being a housewife, where she happens to enroll in Eric's class and proceeds to embarrass him. However, it's unclear if she stays in the class or not because it isn't brought up again after that episode.
After she gets fired from the car dealership in the fourth season of The Middle, Frankie decides to go back to school and train to be a dental technician.
Modern Family did this a little differently. In the fourth season, with Lily now in kindergarten, Cam decides to go back to school ... as a teacher, replacing the fired music teacher (only at this point in the series did we learn he had been a music teacher before, although there had been a hint in the second season when he took over as director of Luke and Manny's class production).
A recent arc in The Big Bang Theory has Penny enrolled at a history class at the local community college. If Leonard's assessment of how bad her paper was is to be believed, there's a reason she dropped out of college in the first place...
She also made her female friends write a paper for her.
In Avenue Q, There is the song "I wish I could go back to college" In which Nicky, Kate, and Princeton say they wish they could go back to college and in the end they all decide they'd be losers if they went back, because they would be thinking "these kids are so much younger than me"
There was an earlier episode where he had to take a night course run by his old high school principal because he never finished remedial science. His final exam gives us a classic:
Homer: All right brain, you don't like me and I don't like you, so let's just do this and I can get back to killing you with beer.
Homer's Brain: It's a deal.
A Family Guy episode revolves around Brian returning to Brown University after it's revealed early in the episode that he dropped out, and The New Yorker doesn't hire anyone without a college degree. Mentioned later in "Jerome is the New Black" when Quagmire chews out Brian on everything that he hates about him, one of which is that Brian "...failed college twice, which isn't nearly as bad as your failure as a father..."
Inverted when Stewie, the infant, also poses as a high school student to show Brian how easy being cool is. He succeeds, and even wins the heart of the hottie Peter dated, unfortunately, being an infant, he wasn't well endowed, so she dumped him, and he got her taken away on child molestation charges.
Peter also had to go back to school and finish the third grade in order to get a promotion at the brewery. Hilarity Ensues and like in the toad episode he starts believing he was a real third grader and acting as such, including getting Quagmire to pose as his father so he could leave school to attend a ball game.
A small gag used in a third season episode when Peter is about to be killed by a bear while on a hunting trip with Chris, his childhood flashbacks appear showing he has to repeat the fourth grade several times and finally passed right before his hunting trip.
In the TaleSpin episode "Sheepskin Deep", Baloo returns to finish school so he'll be able to attend a class reunion. The really hilarious part is that it's elementary school, the same one Kit attends, and we see him trying to fit into the tiny little desk and everything.
An episode of South Park has Officer Barbrady go back to school—and the third grade no less—after it's revealed that he's illiterate.
In an episode of Hey Arnold!, Arnold's 81-year-old grandfather, who dropped out due to the Great Depression, goes back to elementary school. He quickly advances to the sixth grade, and then becomes a delinquent, before becoming a good student again and graduating.
Lampshaded in the episode of Futurama where Fry has to prove he has what it takes to be a College Dropout after Leela told him that the increase in education standards put him on the level of a high school dropout. He was formerly a dropout of Coney Island University (Go White Fish!)
The Flintstones had an episode where Fred has to attend classes in high school and it's a struggle. However, he's a whiz in the local geology course, which he notes he learned the hard way considering he works in a quarry.
Done in an episode of Johnny Bravo, "Prep School Johnny". Johnny goes back to school because he didn't finish a class. Hilarity Ensues.
Cat of CatDog must complete one final day of high school to graduate.
Beetlejuice in the cartoon, has to finish kindergarten in order earn his license back. His license to drive people crazy, that is.
I Am Weasel and I. R. Baboon had to return to third grade because of a typo. If they don't, Weasel won't be allowed to keep his Nobel Prizes and Baboon won't be allowed to keep the banana he got as a consolation prize. Weasel's tendencies to overcomplicate third grade questions made it hard for him but they eventually passed. However, someone pointed out another typo, showing it was fourth grade they hadn't finished. It was revealed the Red Guy was the typist.
An Al Brodax Popeye cartoon had Popeye consigned to school after Olive spurns him for being an "uneducated ignoramus." He starts at grade 7, but his constant hilarious answers for basic questions cause him to regress a grade each time until he winds up in kindergarten.
7th grade teacher: What did Caesar say when Brutus stabbed him?
Popeye: He said, "Ouch!"
6th grade teacher: What is the difference between a verb and an adverb?
Popeye: A voib is an animal, and an advoib is a female voib!
In God, the Devil and Bob Donna has gone to college (presumably not able to go while she was pregnant with the kids) and has some trouble picked a major because she's worried she won't get another shot at it. Bob reminds her she will always have another shot, she's earned it.
In The Fairly Oddparents episode "The Old Man and the C Minus", Timmy's Dad entered a Game Show titled Are You Brighter than a 4th Grader? and lost because he answered "sea cucumber" to all questions except the one where "sea cucumber" was the right answer. He then admitted he didn't finish fourth grade and his wife forced him to go back to school to set an example for their son.