A variant involves the Quirk being useful but not in the battlefield, like some kind of healing Quirk or sensory powers.
Other cases have Midoriya simply be a rare, late bloomer in terms of his quirk activating, and that it simply kicks due to a random event after his canon diagnosis as quirkless, or receiving One For All acts as a catalyst to awaken his initial quirk.
Midoriya receiving either his mothers quirk, (but significantly strengthened to the extent of full-on telekinesis), or his currently-unseen fathers fire breathing ability.
Among the "Midoriya with a quirk" stories, Midoriya having Mirko's quirk has become popular recently, due to the Fanon of Midoriya's rabbit motif and Mirko's popularity. This sometimes includes on him getting an outfit based on her, which sometimes is a Leotard of Power too.
One of the most popular fanfic ideas is to give Izuku the superpowers of a popular comic book hero like The Flash or Spider-Man separate from a Quirk, potentially using them in tandem with One For All.
It has become somewhat popular to write fics where All Might is Midoriya's secret father or even that Midoriya is All Might's publicly known son. It's common to put this in Inko/All Might fan works, which is a ship with a sizable amount of fans. A minor variant of this is "All Might acting like Izuku's Dad," where the difference is that All Might merely acts like a father figure to Izuku, rather than outright being his father. This doesn't exclude stories where All Might becomes Izuku's stepfather, though.
A popular Alternate Universe is the idea that Midoriya would become a Villain rather than a Hero, inheriting All For One and often becoming a superior, if not someone competing with Shigaraki for dominance over the League of Villains. Often, he becomes Bakugo and Todoroki's Nemesis. That AU usually has Midoriya descending into insanity and becoming a very capable murderer of Heroes, though keeping his Hero Otaku qualities, usually he wears barman clothes akin of Kurogiri's and is a friend to Himiko and Dabi. There are enough fanfics with this plot to warrant its own folder on the Fanfic Recs page of this trope.
While not as popular as showing him as a Villain, Midoriya as a Vigilante has some traction, specially after the Spin-Off series My Hero Academia: Vigilantes was released to showcase the life of the Vigilantes. In some of these Vigilante fics, Midoriya may team up with Toga and Dabi who were given an Adaptational Heroism treatment. It's also semi-popular for him to form a Power Trio with Shinso and Hatsume, particularly if he still winds up attending U.A..
Midoriya staying Quirkless and taking All Might's advice about becoming a police officer if he really does want to help people is a common plot that is quite popular in some circles.
A particular dark and angsty fanfic plot is one where Midoriya takes Bakugo's advice from the first chapter and commits suicide (almost always by jumping off the school's rooftop). How the story goes from there varies, but almost uniformly, they either follow Bakugo becoming guilt-ridden about causing this or Midoriya faking his death and becoming a member of the League of Villains. Sometimes, these two merge to form a story where a guilt-ridden hero in training Bakugo meets Midoriya, who he thought to be dead, as a villain, and tries to either turn him into a hero or is manipulated into becoming a villain.
"Dekubowl". There is a plenitude of fics where several characters compete for Midoriya's affection. Todoroki, Uraraka and Bakugo are almost always participants, but the entirety of Class 1-A are available contestants, as well as Mei, Shinso, Toga, Shigaraki, Mirio and so on, truth be told, any given character introduced is a possible addition to Midoriya's fanon harem.
There are quite a few plots about Midoriya's childhood, in particular, how would his childhood go if someone else was his Childhood Friend instead of Bakugo. Usually, Shinso, Iida and Todoroki are the ones used for these plots. Less common but also abundant, is Midoriya having a childhood friend with an OC.
Midoriya meeting All Might far earlier than in canon, receiving One For All, and allowing him more time to learn and master it far better than he has been doing, avoiding or lessening the crippling injuries he runs the risk of canonically.
A popular villain quirk to make fics about are ones where they turn Midoriya into a girl. More rarely, this sometimes happens to Bakugo.
Because of the sheer ridiculousness of the medical test (so apparently an extra joint determines the chance you'll grow a tail), some stories have this practice either be a sham, or an archaic way that isn't supposed to be used anymore. This is also a great way to have Izuku have a Quirk all along.
It's rather popular to have Izuku hide the fact he was being bullied from his mother.
In fanfics that have Bakugou's bullying revealed it's fairly common to Izuku being one of his defenders to the point that fics have Izuku convincing the likes of Aizawa or Nedzu to not expell Bakugou on the grounds that he was a product of his environment and deserves a chance to change.(Ex: Deku? I think he's some pro...)
As a consequence of above, it's rather usual that whoever learns about what happened to Izuku ends up hating Bakugou for it, Uraraka is the popular candidate of this though it's also extended to other characters like Shoto or Iida.
Related to above, it's pretty common to depict Izuku as suffering from depression and/or severe self-worth issues due to a lifetime of bullying (often at the hands of Bakugou), even going so far to mention that he did thought about jumping off the school's rooftop before changing his mind, whether through Bakugou's actions only or as a product of All Might's words.
Midoriya having his past Quirklessness revealed to others. This can be voluntarily told, or discovered by others. It is regularly Aizawa that finds out since it plays towards a Dadzawa scenario. It can also branch into an exploration of discrimination against the Quirkless.
If it happens without revealing the secret of One For All, he'll usually tell a half-truth about how his body needed to be stronger before he could use it.
Due to the popularity of Hero Class Civil Warfare, it's becoming more common to see "Hero vs. Villain" training exercises pop up to show characters like Izuku or others act like villains without having a true change in morality.
A particular take on Fanfics centered on the UA Traitor is to have Midoriya be wrongly suspected of being the traitor. This is commonly caused by people discovering his analysis notebooks detailing the weaknesses of his classmates. Alternatively, someone who isn't in on All Might's secret could learn that Midoriya used to be Quirkless and come to suspect that All For One gave Midoriya a Quirk. Sometimes both of those ideas are used at the same time to make Midoriya all the more suspicious to the accuser.
A highly specific form of Adaptational Early Appearance is Hatsume Mei confronting Izuku when he cleans Dagobah beach because she's upset he's taking the scrap she's using to make her "babies" which appears in a lot of different fics such as Total Command.
Plots related to the characters' future as Pro Heroes are common subject in fanfiction, whether or not it includes shipping.
It has become popular to write about Eri's future after the Internship Arc, particularly, her relationship with Deku, Mirio and even Nighteye. Some believe she'll be adopted by either Inko, making her Midoriya's little sister, or Aizawa due to their similar Quirks.
As Midoriya keeps befriending children who look up to him, Kouta, Eri and Katsuma, stories about them going to U.A. and trying to become heroes to follow their idol also become more popular. Sometimes this also has them interning under a Pro Hero Midoriya.
CrossoverFanfics where Midoriya meets and fanboys over other known heroes also exist. Things like meeting Superman, The Incredibles, Spider-Man, etc are common plotlines. An entire block of most crossovers with the latter often entail Spidey being dropped into the world of My Hero Academia to become a student in U.A. Other depict these more experienced heroes as members of American agencies who often are depicted as being some of the most experienced pros in the world. In the event most characters like the aforementioned Spidey do not get an Age Lift to match the ages of the U.A. students, their younger Legacy Character counterparts (Miles Morales, Robbie Reyes, Kamala Khan) take the spotlight instead.
Plots Focused on Side Characters
Due to Mineta's large hatedomdue to his perverted antics and lack of depth and Shinso being a far more populartragic boy who wants to be in the Hero Course, several people who write fics prefer to simply write as if Shinso is part of 1-A instead of Mineta and just forget he exists all together. Sometimes, when he is acknowledged, he is described as being widely disliked by his classmates who are glad he left and receive Shinso with open arms. When Mineta is even acknowledged, the typical way of replacing him with Shinso is to have Mineta finish last instead of 2nd to last in Aizawa's quirk apprehension test on opening day and thus get kicked out of the hero course, since the only reason Midoriya didn't suffer this fate in canon is that he impressed Aizawa with his combination of resolve and cleverness. Alternatively, Aizawa learns of Mineta's sexual harassment and creeping on the girls of 1-A and swiftly moves to expel him. Notably, this is so common that variants of it (including "Mineta Minoru Doesn't Exist", "Shinsou Hitoshi Replaces Mineta Minoru", and "Mineta Minoru is Expelled from U.A. High School") are all dedicated tags on Archive of Our Own.
A trend in fanfiction is the idea of Hisashi Midoriya, Izuku's father, being a Villain, expanding why he hasn't shown up or take an active role in being a father figure to Izuku for years. This follows from the theory of Dabi possibly being Izuku's father but instead of using the theory completely, it changes the theory that Dabi is a different person from Hisashi. It has become especially popular to have Hisashi and All For One be the same person.
In Alternate Universes where Deku doesn't inherit One For All, the most common person to inherit it in his place is Mirio, as All Might was going to meet him to see if he was worthy before his chance encounter with Deku.
Melissa Shields inheriting One For All is also gaining popularity.
For whatever reason, many authors like to pretend all the adults are in the same age range and went to school together. While this is canon for Midnight, Eraser Head, and Mic, putting All Might and Endeavor with them is quite a stretch.
Something that is even used by Horikoshi himself in the side materials is to make Villains with weird Quirks that can kick-start a plot by affecting one of the main characters, the author used it in the "Smash!" comics to make a story about Bakugo acting as classic BishōnenLarge Ham due to a Villain's Quirk. In fanfiction, this is often used in PWP with a Villain having a lust-inducing Quirk. This was even the plot of an OVA, as there was a person with a zombie-making Quirk.
Group chat fics, which are Script Fics where the framing device is that they're a transcription of internet chatroom logs or text group logs of the main characters. Like real life group chats, they often tend to be heavy on meme humor and light on plot.
Bakugo having a Hair-Trigger Temper is canon, of course, but many stories have him erupting and doing something terribly awful because "stupid Deku" committed the grievous crime of existing one time too many. What happens afterwards tends to be dramatic more often than not.
Aizawa's canonical actions as a deconstruction of the Sink-or-Swim Mentor are pretty often taken to task. While the canon makes note of various details that paint his methods as probably a bit too extreme even In-Universe, they are often also given a "but dammit, they work!" counterpoint note It's since been revealed that this is really just a Scare 'Em Straight tactic: he was given authority by Nezu to expel and then re-enroll students whenever they want, allowing him to use the threat of expulsion as a very real potential punishment, then immediately re-admit them after they've learned their lesson - though, they still have to live with an expulsion in their permanent records. He's also given the motivation that his childhood friend Oboro died during his own internship, driving him to push his students harder so they won't meet the same fate.. Not so much in fan fiction, when stories in which he's sympathetic give him a "dude, are you freaking CRAZY!?!" speech from others or have Aizawa himself mention that these are methods that were stupid to begin with and cannot be applied in this instance (whatever happens in the fic) anyway, and in stories where he is unsympathetic he is painted as an inefficient jerk at best and a monstrous asshole at worst. Some people in the latter camp, such as the author of Coyote, even go so far as to claim that Aizawa only keeps prodigies who are so talented he won't have to work very hard to train themnote Which, again, doesn't hold up in light of the revelation that he didn't actually expel anyone.
Bakugo assaulting Midoriya at the beginning of the Final Exam battle against All Might is a moment that gets focused on in Fan Fics that target Bakugo being a Jerkass, Aizawa's Sink-or-Swim Mentor methods, and the School Bullying Is Harmless idea. It gets portrayed as the moment where Midoriya snaps from the abuse and abandons Bakugo to win the exam by escaping alone. The consequences of the actions vary, but what usually follows is All Might being disappointed, Bakugo being angry, and Aizawa's response to the events. As noted under Aizawa's entry above, his response depends on how sympathetic the author makes him.