Accelerator: A young man who's trying to redeem himself for the terrible things he has done while trying to avoid turning back to his past self or a sadistic heartless monster who hasn't changed his ways and enjoys being a powerful killer?
Another (albeit related) point of contention about Touma is just how much of a character he is, or whether he is a character at all and not just a plot device. Some people have noted that even though he always saves the day, he rarely if ever has actually any personal relation to the problem at hand, and that the conflict could have been handily solved by any other sufficiently strong character that just happened to come along, and have argued that this makes him something of a Satellite Character in his own series. Said people are also somewhat divided whether this makes him a Black Hole Sue or not.
The Chris Carter Effect: A frequent phenomenon among fans. The series has by now introduced so many plot-relevant characters with even more potent powers with their own storylines that many people have trouble keeping up even with character charts. Combine this with the fact that the revelations about Imagine Breaker and the way Espers work have been minimal so far (and many other less important questions haven't been answered either, but rather just raise new questions) and that Character Development has been all but non-existent for the majority of characters as of late (including main character Touma), and that the staff seems to be more interested in working on the spin-offs rather than the main story, and you have a giant chaos that has little potential of eventually wrapping itself up completely.
It doesn't help that literally more than half of the episodes of Railgun are anime-original, created because the director wanted more moe elements in the show and to force in happy resolutions that didn't exist in the manga.
Complete Monster: Terra of the Left is a murderer and a member of the elite Vatican unit God's Right Seat. Unlike his less psychotic colleagues, Terra exists only to kill those who aren't Catholic, not even seeing them as human beings. To assist in regaining his power, Terra outright slaughters a host of tourists, including the children, which prompts his comrade, Acqua of the Back, to turn on him. Terra's goal is no less than the utter genocide of every man, woman and child who won't serve the Vatican.
Critical Research Failure: The reason why Stiyl looks so old despite supposedly only 14 was because of a miscommunication between the artist and author: Touma and Stiyl's first confrontation was supposed be something of an Old vs New (which the artist took literally to mean "old man vs. young boy"), completely missing the note that said Stiyl was only 14.
Kazuma Kamachi noted in the afterward of NT 12 that to him, Frenda Seivelun was just a one-shot character to be unceremoniously killed, and did not anticipate that she would be so popular to the fans. This led to her getting a big role in Railgun and to her becoming a major plot point in NT 6 and 12 despite being long dead.
Now with the second season of Index, Fukiyose Seiri has become very popular with fans on her debut in Episode 8.
Accelerator has a huge fanbase due to how Ax-CrazyAwesome he is, to the point that a large amount of fans claim HE should be the main character, not Touma.
Fanfic Fuel: The sheer size of Academy City, the number of unresolved plot threads, and the nature of Esper and Magic powers involving practically every area of physical science and fairy tale imaginable provides ample room for creating OCs and new storylines by eager fans.
Fanon: Fans have speculated that the Amakusa Catholic girl that Touma fought and saved from a fall in Volume 7 may be Itsuwa, the Amakusa warrior who was first introduced in Volume 11 which may explain why she has a crush on Touma in the first place. However, the 2nd season anime had it Jossed as it wasn't Itsuwa that Touma saved but another girl.
It's also fairly common fanon that Laura Stuart is Index's mother, especially since the two are specifically drawn to resemble each other. This also adds an extra Kick the Dog element to Laura's treatment of Index if you buy that theory.
Fans have theorized for years that Aogami Pierce is the sixth level five, by this point they would be furious if it turned out it wasn't him.
"Funny Aneurysm" Moment: Index-tan Episode 2: Himegami is asked what her wish for the second season is. Her response? "Um, I won't ask for my episode, but I just want to be treated more-". Guess what happens in her first lengthy appearance in Season 2? She gets filleted by Oriana Thomson because she thought that Himegami was an agent of Necessarius due to the Celtic cross around her neck.
The Great Politics Mess-Up: Britain allies with China and India to take on France and Russia in World War III. Note, Britain is an ally of France (been one for over 100 years now), China isn't allied with Britain at all, and the fact is that Russia, even in its present state, could curb-stomp Britain with barely any trouble, as well as India (who happens to be Russia's primary weapon importer), and France as well.
Harsher in Hindsight: Academy City's Power Curriculum Program. In theory anyone undergoing this program can become an Esper yet there are still people who have yet to gain powers and even those who did never go a higher level which suggest the program has some problems. However Vol. 22 reveals the program is secretly being undermined by the Higher Ups of Academy City who decide who can and cannot gain Esper powers and/or go a higher level based on the type of the powers that person has. This revelation makes it much worse once you realize Level 0's like Saten, the Skill Outs gangs and low level espers like the Level Upper users, who work hard to gain powers/higher levels but never can because their training is being sabotaged as the Higher Ups see no point of helping anyone who doesn't have the powers they want. That's right, the city is responsible of destroying the dreams of many students and leading them into path of cynicism and crime.
All intentional; while Mikoto claims in SS: Liberal Arts City that Academy City has no intentions of taking the world via military force, the revelation via Chapter 22 suggests otherwise. Why else would you try to make an army of level 5s or an "interceptor" aircraft that has the ability to fly halfway around the world and level a city single-handedly? Basically, the reason why the corporate crooks of AC haven't bothered leveling the level zeros of their population isn't just because they don't want to, its because they need cannon fodder; they needed a group of disgruntled individuals who they knew would resort to violence in order to defend themselves against those termed and rewarded for being genetically superior, so that they might label that group as people on whom it is okay to use your powers, people whom it is okay to murder, because no one will care about them due to their collective reputation.
Hilarious in Hindsight: This AMV shows Accelerator as a singer of rock band. Then in 2015, came a new spin-off manga titled "To Aru Idol no Accelerator-sama" staring Accelerator as an Idol singer.
"Holy Shit!" Quotient: A large portion of the series, but the entirety of Volume 22 and New Testament Volume 9 are probably the biggest. Especially NT Volume 9.
Every new book (except arc finales like Volume 22) usually makes the "Holy Shit!" Quotient go way higher than the previous book. NT Volume 10 takes this to an extreme arguably outdoing even NT volume 9 with its insanity especially in its epilogue.
Iron Woobie: Touma gets his ass kicked on a regular basis, and even the fights he wins tend to end with him in the hospital. There's no real explanation for why he puts himself through such misery, especially considering he has his own inherent bad luck to deal with. And yet he claims to be happy with way he lived his life...
But he always does win in the end, and women fall like flies to his two-dimensional Shonen Protagonist hero speeches. What's not to be happy about?
The novels explain all of this in detail... eventually. Volume 22 summarizes it quite nicely, though NT volume 9 best outlines his "real motivations." NT volume 9 partially trolls and explains that Touma doesn't really believe half of the "hero speeches" that he gives to villains. He just does this to briefly get through to people who have temporarily gone crazy as a result of experiencing severe loss/tragedy in their lives. As of NT volume 9, he has a higher moral ground and it is actually justified because of what he went through...
New Light, particularly Bayloupe and Lessar, though Floris and Lancis aren't exactly innocent either. The group seems the be well aware of their apparently abnormal closeness too.
Floris: "Hey, you two lesbians who look like you’re from some erotic novel or something." note Said when Bayloupe and Lessar were in a compromising position in the back seat of a car.
Lessar: "Floris! Lancis!! Quit awakening strange new tendencies and wake up! We need to use this room!!" note Said when Lessar found the two sleeping in the same bed when she needed to have a chat with Mikoto. Apparently Floris just likes to crawl into other peoples beds when sleepy.
Special mention goes to Komoe-sensei, which is even in her name. She's also not above invoking this trope in order to guilt her students into doing things.
Quite a few of the Sisters, but 19090 stands out. She's a minor side character, but in her first appearance (when the four Sisters still in Academy City were getting sized for their winter uniforms), the others discovered that she wasn't quite as identical as she was supposed to be, due to reading girly magazines and dieting. She runs away tearfully, while her Sisters hunt her down ruthlessly in an attempt to measure her more precisely and force her to fix her eating habits.
The researchers involved in both events under the For Science! entry above cross this line in a big way.
Then there's the #2Level 5Teitoku Kakine. He's Obviously Evil from the get go, but he still manages to be personable enough that you aren't quite sure what you think of him. That is, of course, until he beats up Uiharu, earning him the hatred and rage of the majority of fans. It could have been worse though, it didn't break or kill her.
Apparently, Accelerator can state-change air into plasma by making ridiculous noises with his mouth, another form of his evil laugh. This is also a case of Formulaic Magic; those noises he was making were Accelerator performing the calculations necessary to use his Vector powers at high speeds... which does nothing to make them less ridiculous. Things get even more hilariously confusing when it is later revealed that those sounds are in fact a very basic form of the language spoken by Holy beings such as angels, which is why he's able to harness so much extra power whenever he makes them.
Every feeling of suspense or mystery when Kazakiri's Artificial Angel form appears is destroyed when they show her face, with her tongue hanging out and her eyes rolled back up. It doesn't help that it looks exactly like the so-called "ahegao face", a common and rather memetic phenomenon in Hentai, which just makes it look even more silly and out of place.
Never Live It Down: No matter how much good he does or how many heroic acts he does, some fans still hate and can never forgive Accelerator for the terrible things that he's done, especially what he did to the Sister Clones before his Heel–Face Turn.
The Scrappy: Shiage Hamazura. There are some reasons some people dislike him. He's not that attractive, he's a Level 0 with no cool powers unlike the rest of the male characters of the series, and he's the servant boy and Butt-Monkey for Team ITEM. It didn't help that he defeated fan favorite villain Mugino and scarred her, which brought him a lot of hate from her fans!
It's rather surprising how many fans are starting to pair up Fiamma and Carissa, considering their single canon interaction was an I Shall Taunt You on Fiamma's part.
Some of Touma's ships can be like this, since the most you can say of some of their interactions is that Touma punched them while giving them a dressing down (such as Vento x Touma or Carissa x Touma). Heck, some of them haven't even had an embarrassing perverted moment with him in canon yet!
Ship-to-Ship Combat: Which girl should be with Touma? Don't ask! because the moment you say so, you will get yourself in a nasty Ship-to-Ship Combat between other fans over their favorite girl!
Yet two of the biggest Ship-to-Ship Combat by Japanese fans are the Mikoto x Touma fans and Kaori x Touma fans. These two fanbases are so big, the novel artist Kiyotaka Haimura knows it and even drew about it!◊