The first real fight, the one between Stiyl and Touma, is pretty cool in the anime and manga. But in the light novels it's narrated from Stiyl's point of view, and we see how a magician views Touma and why he becomes The Dreaded. At one point, Stiyl seriously thinks he might be fighting God.
The ending of the fight where Touma destroys Innocentius with an Offhand Backhand before running up and punching Stiyl out.
When Touma and Stiyl face off against Aureolus Izzard, a Reality Warper. After immobilizing and toying with them, he instantly completely removes all of Stiyl's skin and severs Touma's right arm, the source of his power. Touma cuts off Aureolus's subsequent Evil Laughwith an Evil Laugh of his own, walking steadily towards him—blood squirting out of his stump—with an insane smirk on his face and mocking Aureolus's frantic attacks as they pass right through him or are otherwise negated. Turns out that Aureolus's power was controlled by his thoughts, and Touma's insane behavior so terrified Aureolus that he started believing that his incredible powers had been rendered completely ineffective. By the time Touma reaches him, his imagination has granted Touma a huge dragon head in the place of his missing limb. Even after seeing his companion's skin ripped off and getting his special arm chopped off, Touma was still able to bluff his way to victory with a Slasher Smile on his face.
Before that, the 13 Knights of the Roman Catholic Church blow up Misawa Cram School... only for Aureolus to literally reverse the damage and annihilate the Knights.
The reality warping technique, Ars Magna, was thought to be impossible because one needs to chant for 100-200 years to get it. Aureolus cut that time drastically by brainwashing everybody in Misawa Cram School to chant for him.
Misaka Imouto using her powers to make ozone in an attempt to suffocate Accelerator. He saw through the tactic and attacked her, but he complimented her on finally figuring out a way to hurt him.
During Touma's fight with Accelerator when he starts making plasma, Sister's make good use of their powers by making wind turbines turn dissolving Accelerator's plasma in the process. Complete with Theme Music Power-Up!
Touma's fight with the Unabara impostor in the construction site.
Touma blocking the giant stone golem Ellis' punch with one hand.
Index herself gets one when, after discovering her Sherry Cromwell decides to use her golem to attack Index and get the 103,000 grimores that she has memorized Index then shows even without going into her emergency survival mode she has complete control over those grimores and uses them to show that the giant golem she is fighting and that Sherry's abilities aren't even on her level as she proceeds to methodically destroy the golem all while the song Jellyfish plays in the background.
Touma's Big Damn Heroes moment in episode 26 of Index, when he comes out of no where and defeats the enemy with a single punch, all while reassuring a friend. Nice.
Touma saving Kuroko by leaping up using furniture thrown up by Mikoto was epic. Finishing it by punching a partially teleported object backwards through dimensions. There are no words.
Immediately after above scene, Awaki was seen escaping Cue Accelerator, of all people, showing up to wreck Awaki in the face.
Volume 7: Touma finds out he's been tricked into handing a woman over for execution to the Roman Catholic Church and charges into their local HQ, alone, to declare war on an army of 250 killernuns while they're kicking the dog.Good Is Dumb, but that doesn't make it any less Badass!
Touma: What should I do? WHAT NONSENSE, OF COURSE I SHOULD SAVE HER!
Touma knocking Biagio Busoni's giant cross away with his left hand.
Aleister: Seems like there's some commotion outside...
In the novels, although he doesn't throw an entire building, he borrows a huge amount of energy from the planet's rotational vectors to fuel his attack - enough to slow it down by 5 minutes.
And as a testament to how implacable Aleister's fortress is, the building remains unharmed. To hammer in the point, Accelerator's attack used enough energy to slow down the Earth's rotation for five minutes!
Accelerator awakening for the first time and reducing Kihara to plasma. Soundtrack Dissonance that could put Evangelion to shame? You bet!
The Academy City Invasion arc as a whole can be considered a single Crowning Moment of Awesome for anyone involved. Especially for Accelerator.
Accelerator outwitting the leader of Skill-Out and defeating him. Touma vs Hamazura, a few minutes after Touma had been shot in the side.
Mr. Misaka's phone call in the end of SS2, asking someone at Academy City why girls who look exactly like his daughter have been attacking military and research targets (in an attempt to rescue the gemstones). He makes remarks about what he'd do to anyone hurting his daughter, and then the truly awesome part hits: He's talking directly to Aleister. Yes, that's right. A wandering consultant is threatening possibly the most powerful man on the planet.
Volume 14: After Acqua of the Back learns that Terra of the Left slaughtered a bunch of tourists, even the children, Acqua punches Terra so hard he breaks in half at the waist. Acqua leaves Terra to bleed out, and tells him to go to Hell.
Volume 16: Touma showing up to saveKanzaki and the rest of the Amakusa Catholics from Acqua of the Back when he is already heavily injured from a fight with the same person. Not only that but this gave the Amakusa Church a chance to take down Acqua with a Heroic RROD-inducing spell.
Touma proves in Volume 17 that despite his label as one of the idiot trio, he's much smarter than he lets on. He pulls one over a terrorist by pouring boiling tea into a narrow air vent and causing it to expand, making the terrorist on the other side think that there's someone inside the air vents. The terrorist decides to check the air vent... and gets boiling hot tea poured on his face. This, by the way, was meant to distract the terrorist so Touma could enter the cargo hold through the door safely. Also, he ends the fight by giving the terrorist a lesson on thermodynamics.
Volume 18: After Fiamma steals Index's remote control, Touma simply says: “Stiyl,” Kamijou called out to the red-haired magician. “I’m gonna go punch Fiamma. While I’m gone, you take care of Index.” BADASS!
Volume 22: Touma drops the "Star of Bethlehem" on an Archangel. And because this was not enough, he runs through the entire thing at the same time, so HE COULD PUNCH THE ARCHANGEL PERSONALLY!
Also, when Fiamma of the Right severs Touma's right arm and absorbs it, becoming La Persona Superiore a Dio aka The Person Higher Than God. Fiamma gloats and attempts to kill Touma, but "The Invisible Thing" emerges from his stump, terrifying Fiamma. The dragon attempts to kill him, but Touma declares that he doesn't need its help and absorbs him, regenerating his arm. He proceeds to talk to Fiamma, making him doubt whether his plan was actually worth it, then charges up and punches him out.
This might have more repercussions than you would think. By New Testament 2, Aleister is backed into a corner so deep, he took NO actions out of fear of disrupting his plans further, even when AC was about to be destroyed.
In the Short Story, Uiharu SS, Uiharu jumps atop a vehicle that's moving at 120 kph, then ties herself to it and uses a parachute to turn herself into a human brake!
New Testament 2: Birdway got away with trolling Aleister, and pretty much ensuring that Touma, Accelerator, and Shiage will involve themselves more in the next battle using her skills at analyzing charismatic figures. No wonder she's the author's favorite.
In New Testament 3, she's even more Badass. The other heroes are facing a magician who's basically Cinderella and curbstomping everyone, when she simply hits her with a Tanker truck and then blew it up.
New Testament 4: One-Eyed Othinus curbstomps everyone, even Touma. She severs his right arm, but when "The Invisible Thing" emerges from the stump, she curbstomps it too!!! Then, Ollerus and Fiamma of the Right arrive and manage to fight her to a draw and make her retreat.