Aquaman stopping◊ an army's actions simply by arriving on the battlefield. Don't even think about picking a fight with the king indeed.
During the JLA Mageddon event, he single-handedly pacifies his own people driven to violence by the Warbringer, then mobilizes the Atlantean military to forcibly stop the global conflict until the various Heads of State are convinced to call a cease-fire.
DC vs. Marvel, and literally dropping a whale on Namor.
During Brightest Day, Aquaman is tasked with finding the new Aqualad, Jackson Hyde, before he is captured by Siren and Black Manta. Black Manta finds him first and is about to kill his adoptive father.
Black Manta: He is not your father. He is nothing more than another man I've killed.
(He shoots some sort of wrist harpoon at Jackson's dad's face, and just as the object is half an inch from his face, fucking AQUAMAN catches it and breaks it with one hand.)
Black Manta: Aquaman.
One of the absolute best, though, is one in which he isn't even present: at the end of Patton Oswalt's Justice League: Welcome to the Working Week, the Big Bad, despite having just been beaten, is gloating that it nevertheless took the entire Justice League to do so. The Big Bad then laments, "I'm saddened... your Sea King isn't here". The response is "You're lucky our Sea King isn't here!◊", because if he had been, the beating would have been that much worse...
Near the end of PAD's run, Triton has killed Poseidon and is kicking the crap out of Aquaman and friends. Aquaman lets Triton kill him, so he can get to the afterlife. Once there, he decks Charon, rallies the souls who didn't have boatfare, jacks Charon's boat, runs Charon over with his own boat, storms the literal Gates of Hell, cuts off one of Cerberus' heads, marches right up to Pluto and demands Poseidon back, ultimately convincing Hades with a very solid Batman Gambit. On his way out, Cerberus is back, and Aquaman has just one word for the titanic guardian of the underworld: "Stay."
In the first issue of Aquaman since the relaunch, writer Geoff Johns destroys the Aquaman jokes and misconceptions throughout. This includes a group of bank robbers laughing at him when he pops in to save the day and trying to run him over with a van, only to get flipped over with the trident, smashed onto the road and tossed into a police car windshield. When Aquaman leaves, the cops joke about how they're going to get made fun of for being "upstaged by Aquaman".
In the same issue, Aquaman is just trying to get some fish and chips (yes, really), only to be harassed by a blogger. From the blogger, we learn that Aquaman is constantly thought of as the Super Friends version in-universe, and therefore largely thought of as a joke. The blogger questions Aquaman's ability to speak with fish (they aren't smart enough to speak, he just telepathically "pushes" them), what he does for money (treasure he finds at the bottom of the sea), and, best of all, how it feels to be "nobody's favorite superhero", to which Aquaman just activates his trident in response.
The New 52's Justice League #6 - Aquaman stabbing freakin' Darkseid in the freakin' eye with his trident!
In Justice League: Crisis on Two Earths, Aquaman is confronted by Captain Super (evil!Captain Marvel) and warned by Batman to "be careful. They're stronger than you are." His response, in classic, Large Ham, 60s fashion? "That remains to be seen!" He then bitchslaps Captain Super across the Watchtower and through a parked jet.
The citizens of Atlantis and the creatures of the sea respect, fear, and love Aquaman more than they do Poseidon. Freaking Poseidon!
EverythingOrmdoes in part three of Throne of Atlantis (Justice League #16).
It's bittersweet, but after the Throne of Atlantis story arc, instead of seeing Aquaman as a joke in universe, the populace is now scared of him.
Silver Age!Aquaman made a hospital to help injured fish.
Justice League Tower of Babel. The entire League, aside from Batman, is hit with tricks and death traps by Ra's Al Ghul that he stole plans for from Batman and modified to be more lethal. In Aquaman's case, he's hit with a version of Scarecrow's fear gas that causes him to fear water, meaning he would eventually die from staying out of it. But he manages to power through and overcome the fear, and then goes on to rescue the rest of the Justice League (minus Superman was only hit with Red Kryponite that drove him away from Earth till it wore off).