The Scarecrow, Dr. Jonathan Crane, is a Mad Scientist dedicated to the study of fear. First appearing in Batman: Arkham Asylum, he participates in Joker's plan to take over the titular asylum and attempts to Mind Rape Batman several times with his fear toxin. Upon his final defeat, he threatens to contaminate Gotham's water supply with the toxin simply to spite Batman. Scarecrow returns in Batman: Arkham Knight as the Big Bad. This time around, he takes advantage of the power vacuum created by Joker's death and unites all the remaining villains against Batman. After a demonstration of his newest fear toxin causes a diner full of people to rip each other apart, Gotham is evacuated, allowing Scarecrow to take over a chemical plant and manufacture a fear bomb powerful enough to take out the eastern seaboard. He even gleefully speculates that the toxin will carry on the air across the county, creating a "nation of fear." Foiled in this, he steals a superweapon called the Cloudburst and uses it to drive all of Gotham temporarily mad with fear. He also has Barbara Gordon kidnapped and leads Batman to believe that his toxin caused her to kill herself. He then manipulates Commissioner Gordon into betraying Batman, and, after the Commissioner goes against orders and seemingly kills him, Scarecrow forces Jim to watch as he drops the still-living Barbara off of a building. In the end, he captures Batman and forces Gordon to unmask him on live TV. He then plans on letting Batman go so he can watch as Gotham is torn apart and everyone he loves is hunted down and killed. All of this was done to completely destroy the myth of the Batman as a savior, and force everyone to experience true fear by destroying their symbol of hope.
Due to being a four-game story, there are details (Batman and Joker's Titan Poisoning in City, Deathstroke's sudden appearance in Knight) that won't make sense unless you've played the other ones.
Some plot points require at least some cursory knowledge of the comic books, though the games rectify this somewhat by giving you profiles regarding characters, but still occasionally falls into this trope, particularly in the case of Jason Todd, whose presence was almost completely absent until Knight.
Ensemble Darkhorse: The Arkhamverse version of Harley Quinn is one of the more popular secondary villains, going from a supporting role in the first two games, to being the Big Bad of her own DLC, to being fully playable in Arkham Knight. Harley's portrayal in the games also raised to profile of the comics version.
Scarecrow. His nightmare sequences in Arkham Asylum were considered some of the best parts in the game. When he was absent in Arkham City, people were disappointed. This may have something to do with him being promoted to Big Bad in Arkham Knight, where he is subjected to a lot of Adaptational Badass-ery.
Poison Ivy could also count. As well as Candy, Tracey, Shiva, and even Copperhead in Arkham Origins.
Foe Yay: All four games illustrate this in Joker and Batman's relationship. Starting early in Batman: Arkham Asylum with Joker: "Tell me Bats, what are you really scared of? Failing to save this cesspool of a city? Not finding the Commissioner in time? Me, in a thong?!" and that the premise of the whole night was a party Joker threw for Batman. Then continuing in Batman: Arkham City with the increasing phone calls from Joker to Batman, the final death scene with Batman carrying Joker out in his arms, and Joker's swan song to Batman. Given their beginnings in Batman: Arkham Origins when Joker's obsession with Batman begins, including his Red Hood story and his mention of "meeting someone very special earlier tonight", and another song for Batman during the credits. And finally culminating in Batman: Arkham Knight with Hallucination!Joker mentioning over and over again being inside of Batman, the heavy indicators that Joker's death affected him so much that he could never return to normal (not even Talia's death is mentioned that much), and the serenade number Hallucination!Joker performed with a little help from Johnny Charisma. Catwoman even makes a dig at the relationship in Knight, and how Batman should stop mourning him and "find new maniacs". The whole Batman: Arkham Series arguably reads like an overall story of Batman and Joker's relationship.
While all the games are generally well reviewed and well received, the prominence of the Joker as really the primary bad guy among everyone else has been criticized, as it lead to the detriment of other villains having a chance at truly taking stage. Origins in particular has a very strong story with or without the Joker being involved, as many fans were excited thinking Black Mask was going to be a more prominent villain than he was. As it turns out, not even being Killed Off for Real in a franchise where he's explicitly stripped of his Joker Immunity can stop him from being a Posthumous Character in Harley Quinn's Revenge and Arkham Knight.
The series and its poor track record with making good boss fights is another example. The original game was criticized for reusing the same bullfight setup with Bane or opting for thug attack waves instead of direct battles for most of its encounters with any other boss fights being deemed lackluster or boring (with the possible exception of the penultimate battle with Poison Ivy). While City was praised for having the famous Mr. Freeze showdown and more original boss fights, overall it remained a criticism due to the presence of several (albeit mostly justified) Anti-Climax Boss segments. Interestingly enough, Origins, a secondary game made by a different studio, was widely praised in its handling of boss battles, making it appear to be an inversion at first. However, Knight notably lacked several proper boss fights with Deathstroke being a notable target of hate while many combat encounters with thugs and Batmobile tank battles filled their place. This in particular has gotten enough backlash to the point of heavily contributing to the game's Contested Sequel status as a result.
Good Bad Bugs: For both Asylum and City, Batman's quick ground takedown consisted of straddling a prone thug and punching him in the head, but due to the target rolling back and forth while dazed, the combat animation could randomly flip him around and have Batman hit him straight in the pelvisor tailbone. While Origins tried to correct this mistake, it also introduced a variation where Batman leaned down and punched the victim's ribs, which sometimes meant he accidentally shoved his face into goons' crotches. It was finally fixed in Knight, where Batman leaps to the side before striking.
Harsher in Hindsight: How shall we put it? The Joker himself has been a Death Seeker from the very beginning of the series. In Arkham Origins, he tries to shoot himself in the head in order to end it all, but Batman stops him from doing so for reasons he can't comprehend. In Arkham Asylum, after the Joker says, "I have nothing left to live for," he does shoot himself, but with a Titan formula gun to the throat. His "suicide" is very painfully slow, as it takes a year for the Titan poisoning to course through his bloodstream before his death and its nature complete their course at the end of Arkham City, in fulfillment of his deserving to die as a monster, all the while Batman is unable to intervene with him.
Headscratchers: How does the explosive gel not blow up inside of the can when Batman presses the button?
The comments section on Destructoid had a Running Gag about which infamous C-list Batman villains they'd love to see in the Arkham games, with the most common target for ridicule being Professor Pyg. Lazlo Valentin would eventually get a sidequest to himself in Batman: Arkham Knight.
There's also the fact that Troy's roles in the Arkham games, along with his roles in Injustice: Gods Among Us & the LEGO Batman games, mean that he's voiced all of the male members of the Bat Family, and a couple of their enemies too.
No Problem with Licensed Games: Not only are these considered the best Batman games ever made, not only are they considered to be among the best licensed games ever made, they're often placed in the top tier of character action games ever made, period. They are arguably the trope's Most Triumphant Example. Related to this is...
What Do You Mean, It's Not for Kids?: It's made perfectly clear that this game series was not aimed at children, with Arkham Knight even getting slapped with an M rating, but that didn't stop kids from purchasing it. The series is full of brutal death, intense violence, psychological horror, sexual content, corruption, and of course Batman and his villains acting more nightmarish than ever before, all packaged along with extremely dark themes and storylines that can be chilling from their concepts alone. There's a very good argument to be made that they are the darkest Batman adaptations ever made. Unfortunately, there were still some families that thought it was okay to buy for kids simply because it had Batman. Needless to say, people were shocked.
This pretty much sums up many fans' reaction to the fact that Commissioner Gordon keeps getting recast. Across the whole franchise, he's had five voice actorsnote Rick D Wasserman voiced a young Gordon in Asylum, but that was Time-Shifted Actor, going from Tom Kane in Asylum, to David Kaye in City, to Michael Gough in Origins and Blackgate, to Chris Cox in Assault on Arkham, to Jonathan Banks in Knight.
There's also the matter of Troy Baker and how many different characters he plays- first he's Two Face and Robin in City, then Joker in Origins, and then the Arkham Knight/ Jason Todd in Knight. That's overall five different characters done by one actor, which had several fans aghast, especially since Baker has appeared in nearly every major video game released in the past four to five years.