Several locations are named after planets from the franchise (eg. "Tatooin Station," "Dagoba Municipal Park," "Hosu (Hoth) City." "Kamino Ward", "Nabu (Naboo) Junior High," etc.). The Hero Killer fight takes place in "Echo Alley", in Hosu City.
Ojiro's hero costume is clearly based on Luke Skywalker's farming clothes from A New Hope.
During the 10-month training before receiving One For All, one of the training exercises Midoriya had to perform was carrying All Might on his back/shoulders similarly to how Yoda had Luke do the same thing in The Empire Strikes Back.
Done at the Dagoba Municipal Park mentioned earlier, no less.
The Power Suit Mei Hatsume tests with Midoriya looks a lot like a bulky Stormtrooper armor, sans the helmet.
Gran Torino's small size and Obfuscating Stupidity when meeting Midoriya are very much Yoda-like. His fighting style also involves bouncing and zipping around whatever area he's in, much like Yoda when he gets serious.
The helmet All for One wears in the Hideout Raid is reminiscent of Darth Vader's, down to the breathing tubes under the chassis.
Nagamasa Mora's hero name, Chewyee, is a reference to Han Solo's nickname for Chewbacca.
Saiko Intelli from anime filler, during the License Exam arc, is possibly a reference to Kamen Rider Build, both having equations float around her to symbolize her intelligence and making reference to a "formula for victory" being set.
Also during the License Exam, an unnamed character seen running toward Tenya and Aoyama looks quite a lot like Ichigo or Nigo.
The Hotta brothers from the Vigilante spin-off are basically a giant love letter to the franchise:
In chapter 101, the part where Hatsume puts Midoriya in an armored suit that nearly breaks his spine is a clear reference to Iron Man 2. The part where she gives Iida gauntlets that launch him into the ceiling may also be a reference to the first movie when Tony Stark is testing out the glove thrusters while building his suit.
At one point, America is referred to as the home of heroes, referencing how the manga's heroes are all inspired by the likes of American comics like Marvel Comics and DC Comics.
Vigilante: My Hero Academia Illegals expands on this. Historically, the system of granting licenses for legalized heroism first originated in Rhode Island, with seven vigilantes being made licensed heroes. This mirrors the origins of the Justice League of America, which started with seven members and were based in Rhode Island.
The official Viz translation of the manga has used the term "Metahuman" a couple of times; this is the catch-all name for superheroes that aren't technology-based in DC Comics.
Chapter 115 seems to be a shout out to Watchmen, with a mentally unstable masked man walking the streets, watching corruption, and monologuing to himself. It's certainly enough of a tone shift from the rest of the series to stick out.
The surnames of David and Melissa Shield, who were introduced in the movie, are likely a shoutout to the Marvel Comics organization S.H.I.E.L.D..
In Chapter 187, Todoroki Rei has a flower from her abusive husband in her hospital room that is implied to be proof of his love, alluding to the ending of the Batman comic Mad Love.
The robot assistants of Recovery Girl bear a striking resemblance to Kelex, Superman's Kryptonian assistant in the Fortress of Solitude.
Detnerat's CEO has a number of similarities to The Joker, starting with his thin build and pointed features. In fact, his very first appearance in a commercial has him making expressions and gestures which are clearly an homage to one of Joker's monologues from The Killing Joke.
Chapter 229 also has a reference to The Killing Joke as it details how Twices life spiraled into villainy with the Jokers iconic All it takes is one bad day quote as the chapter title.
The second movie of the franchise, Heroes Rising, has a woman called Slice among the villains: a redhead whose quirk is using her hair like blades. She's likely inspired by Medusa from The Inhumans.
In Chapter 245, the F Lamming Sidekicks all yell out "Flame on!" when greeting Deku, Todoroki, and Bakugou.
The Sturm und Drang Brothers in Vigilante have an attack formation based on the Jetstream Attack of the Black Tri-Stars in Mobile Suit Gundam, with the three of them lining up in a row and each using a different different "attack" in rapid succession, facilitated by their superior speed and agility. The difference being that the Tri-Stars used actual attacks, while the Sturm und Drang Brothers are just idiotic perverts who in turn flip a woman's skirt, steal her panties, and wear the stolen panties.
Mina Ashido initially chooses the codename Alien Queen. Completely lampshaded. In the manga, she even name-checks the director of the first movie, with her full title being "Ridley Hero: Alien Queen". In a between-chapter panel in the graphic novel collection, she further mentions that she really should have gone with "Cameron Hero", since the queen is from the second movie, which Ridley Scott did not direct.
Power Loader's hero name and Powered Armor gear is a nod to the Power Loader, a similarly powerful yellow exoskeleton.
When Mineta finds a hole in the wall between the boys' and girls' locker rooms that had been covered up by a sign, he says that some of the older students "Shawshanked" their way through the wall, referencing Andy escaping his cell by tunneling through the wall and using a poster to cover up the hole.
In the background, Shigaraki is dressed and barely visible as Predator.
Midoriya is in the middle, dressed as Pinhead and holding the Lament Configuration.
In the background, Jiro, Todoroki and Fatgum are dressed as My Neighbor Totoro, with Fatgum particularly looking the part and even mimicking his format. Ochaco and Mineta are also dressed as Satsuki and Mei.
The second movie got another shout out in the chapter 222 cover, where Midoriya is drawn as Mothra, with Horikoshi joking that that is the key-visual for the movie.
The movie itself features an appearance by a character whos quirk is literally that hes Godzilla. His name, Gojiro (Godzillo) is one letter away in both English and Japanese, and his bio states he's an actor from Japan who stars in Kaiju movies and briefly lived in the US in the late 90's.
The character La Brava has the same name as a book of the same name. The book is about a photographer who starts a romance with an older actress whose movies he loved, similar to how La Brava fell in love with a man who made internet videos and started a romance with him while filming his videos/becoming his partner in crime.
The item Mei is trying out in the woods that is caught by All might seem to be cyberpunk version of a Golden Snitch, likely for Class 1-B's presentation for the Cultural Festival.
Ashido subjects Mineta to what suspiciously looks like the Ludovico Technique in Chapter 217.
Chapter 225, in which Chitose tries to interview Toga, is called "Interview With A Vampire". Hmmm...
When Present Mic is going over the rules of the Mock City entrance exam, he uses silhouettes of characters from Super Mario Bros. as an example, as seen in the page image. Again, the anime throws this out the window due to copyright, but it replaces it with its own rendition of Present Mic in an RPG complete with sprites. However, that didn't stop Horikoshi from introducing Mirio, whose name is a phonetic homage to "Mario", and whose face resembles Mario's beady-eyed toon appearance from Paper Mario.
Speaking of whom, Mirio has been compared to Vault Boy and speculated to be an intentional homage.
While training with Gran Torino, Midoriya attempts to train his use of One For All by wall-jumping. He directly compares the method (repeatedly kicking off walls to ascend) to how wall-jumping works in Mega Man X.
Speaking of Gran Torino, his outfit resembles that of a Mega Man (Classic) character - particularly Proto Man, color scheme aside.
When he lost control of Dark Shadow, it and Tokoyami looked a lot like Eddie and Zato from Guilty Gear.
While touring the rooms, it's apparent that Tokoyami has a replica Master Sword and Hylian Shield in his room; the insignia on the shield is obscured in the dark and the sword is in a scabbard, but the hilt is unmistakable.
The Chapter 120 reveal of the second popularity contest results includes full illustrations of two characters who aren't even from Jump - those being Mega Man X and Pikachu. Because two readers voted for them for some reason.
During the car crash during Chapter 160, Spinner yells out "Grand Theft Auto!" (At least in the English version).
In the second OVA, the kid with the zombification quirk is named Romero.
The victory dance Uraraka, Sero, Kirishima, and Kaminari do after finding out they've all passed the first half of the License Exam is the one from the Yatta! meme. They even chant "Yatta!" in the Japanese version of the anime.
High-End's head looks almost identical to The Guy's, the mascot for Disturbed.
During the provisional license arc, Eraserhead takes Class 1-A to a specialized gym called "Training Dining Land", or TDL for short. Midoriya thinks that it might make "A certain mouse" mad at UA, because TDL is also the abbreviation used for Tokyo Disneyland.
Tomokazu Chikakozu, one of the Meta Liberation Army members, is the company director of Feel Good Inc.. There's even a gorilla-looking man behind him when his name is revealed, to strengthen the reference.
In chapter 226 there is a frame in which Toga and Curious are respectively posed in a similar fashion as Jesus and Mary in Michelangelo's Pietà sculpture. This is used to emphasize that Curious wants to turn Toga into a martyr for their cause.