How about the first two times, of many, that Ranma hands Kuno his ass. They are pretty much the only time Ranma and Kuno have a fight that is even halfway serious. And it shows just how ridiculously powerful Ranma is.
When fighting the biggest head of the legendary man-eating dragon, Yamata No Orochi, Ranma was completely outclassed in terms of raw force, so she opted to prance around in an embarrassing female getup to get the perverted beast drunk or keep it distracted from eating Akane, while Ryoga and Shinnosuke were busy defeating the seven smaller much less formidable heads, and Akane sampled the healing moss from its back. It was finally put to sleep by a magic whistle. What made this both hilariously absurd and awesome is that Ranma stood up to a monster that she couldn't even damage, and was willing to behave in a humiliating manner to keep Akane safe.
And then Akane's own Moment of Awesome when she actually dove into the dragon's jaws in order to save Ranma from being eaten.
And let's not forget Ranma saving an unconscious Akane from the same fate earlier. By swimming all the way to the bottom of a lake that was deeper than the Orochi was tall, grabbing a boulder that was the size of a large car, and smashing it into the Orochi's mouth before it could finish closing its jaws. In his notably weaker female form.
Ryoga's most awesome moment — at least in the manga — might be when he fights Herb's minion, Lime, the likely physically strongest character in the series, and his foe gets the opportunity to put him in a stranglehold after Mousse accidenatlly distracts Ryoga. He has visions of the afterlife for a couple of seconds; then he has a vision of Akane living happily ever after with Ranma and never giving a thought to him again. This makes him feel very depressed.
Ryoga: SHISHI HOUKOUDAN!
And voilĂ - opponent flattened.
A key reason why you don't want to make Ryoga depressed; the Shishi Hokodan is more effective the more depressed you are (and he's got an unlimited supply of depression).
Even more impressive: Prince Herb, an extremely strong chi-user himself, was woken up and awed by the enormous chi Ryoga generated for the gigantic Sphere of Destruction.
Equally awesome was the fact that Ryoga later allowed himself to be buried alive in solid rock with Lime in order to retrieve the kettle that would get Ranma out of Mode Lock. Not only did he risk dying in order to help Ranma, he came charging up from the ground in a truly excellent Big Damn Heroes moment.
His and Mousse's behavior during that last battle against Herb and his lackeys crosses over into Crowning Moment of Heartwarming territory as well, considering that they were doing it because Ranma was serving as a distraction against the much stronger Herb so that they could get the kettle to cancel their own Mode Lock... which was caused by them betraying Ranma to try and cure themselves earlier.
Ryoga gets another awesome Big Damn Heroes moment in the moxibustion storyline, in which Ranma is rendered (literally) too weak to hurt a child. Four of Ranma's enemies take advantage of this by ganging up on him. Just as Ranma is about to be completely overwhelmed, in steps Ryoga, who easily dispatches all four with a seriously badass Go Through Me look on his face.
And when Ranma finally gets Ryouga to come at him seriously (to put this in perspective, the bandanna'd boy shattered the massive boulder they were practicing on top of while honestly trying to apologize for being too gentle-hearted to fight the weakened Ranma seriously), he opens the fight by punching Ranma so hard that the pigtailed boy created a five meter wide crater on the side of the mountain that he'd hit. Ranma got his own Crowning Moment Of Awesome at the end of the fight, however, when he figured out the final step of the Hiryuu Shouten Ha on the fly (because Cologne had forgot to tell him how to do it for real during raining) and hit Ryouga with a blast of cold ki and a tornado strong enough to oneshot his nigh-invulnerable opponent.
The climax of the whole "Ranma's Mother" ongoing plotline, as Ranma leaps off a cliff overlooking the ocean to save a falling Nodoka, heedless of all the cold water below (which would reveal his secret.) Just as he catches her mid-fall, he takes her sheathed katana and hurls it at the cliff-face with such force that it's embedded into the rock, providing a tiny (but adequate) foothold for him and Nodoka, instants before they either splatter all over the rocks or splash into the water. This is followed by the series' Crowning Moment of Heartwarming.
Ranma defeating some of his most dangerous opponents using their own strength, and on-the-fly tactics, against them:
After the monstrous Pantyhose Taro had been extensively battered by both Ryoga, Ranma, Mousse, and Shampoo, Ranma let Taro swing him around on a length of pantyhose, only to use the elastic snap-back to kick the over four metres tall creature back several dozen meters into a hot spring. However, he also had to beat up Taro's even more battered human form right afterwards to finally knock him out.
During Ranma's struggle with the dragon-hybrid Herb, the villain had consistently wiped the floor with Ranma, who managed to stay alive by consistently taunting his foe to be careless, and the narrow plateau — and the mountain it was part of — they were standing on had started to crumble apart from all the blasts. Ranma then used Herb's overconfidence in his ability counter the Hiryu Shoten Ha gainst him, and when caught in the tornado collected Herb's discharged energies from the preceding battle into a gigantic ball of force which instantly KOs the Musk Prince, and then saves Herb's life from the ensuing landslide.
Learning a technique to mostly stay out of sight from Ryuu Kumon's lethal strikes, while loosening the soil around his foe, and then using the vacuum resulting from Ryuu's ultimate technique to summon up a huge surge of dirt that buries the opponent.
Using the phoenix-hybrid Saffron's mountain-top vaporizing flame-generation, in combination with a magic weapon with freezing powers as strong as Saffron's heat (and the ability to block or cut through nearly anything solid), to deliver the most concentrated Hiryuu Shouten Ha in the series, which freezes and shatters his foe.
Then proceeding to throw said weapon with perfect accuracy into a fitted slot on the head of a massive statue that Ryouga and Ranma (who was backed up by the cave-in-clearing force of a Shishi Hokodan) could barely dent, then using the leftover heat from the battle (which was sufficiently hot to significantly slow down his descent) to create a Hiryuu Shouten Ha on the fly that he then used to very precisely punch through the neck of the statue like it wasn't even there and then drop the head on the stump so that the water that would cure Akane would be shot into the air. And let's not forget that the first Hiryuu Shouten Ha that Ranma threw in this fight was sufficiently strong that it rerouted an underground river to Mt. Phoenix, thus possibly preventing Saffron from ever having to use Jusendo again.
Speaking of Saffron... Under normal circumstances, Ranma tends to avoid using anywhere near lethal or maiming force even when his opponents are trying to use instant kill techniques on him. After Akane's life got put on a timer and Saffron stood (well, flew) between Ranma and the cure, Ranma opened up the fight by slicing off Saffron's wings in the middle and dropping him off the side of a mountain, followed up with stabbing him in the arm and trying to freeze the guy to death, and ends the fight with the aforementioned freezing and shattering. Lesson learned: don't @#$% with Akane's life.
Does the anime version, which takes place on a mountain instead of at the beach, count too? When Cologne first gets serious, she conjures a tornado. With nothing more then a flick of her staff. And then we have the equivalent of the Shark Fist battle, with her flying around on the back of a life-sized ice sculpture of a grizzly bear. And telekinetically flinging a few dozen ice boulders at Ranma to boot.
Ranma gets one in the first movie, when facing an opponent too fast to beat with his chestnut-fist enhanced speed, but who is dependent on chopsticks, he punches the ground so hard that the force goes through most of the floors of the tower that they were near the top of and the foundation beneath it to create a geyser that floods the room, then projects the water into blasts that are not possible for Kirin to block.
Speaking of the movies, Ryoga and Mousse each get one in saving the girls the anime typically pairs them off with. Mousse ignores dozens of paralyzing darts to deliver the knockout punch on his foe and save Shampoo in the process. Ryoga stumbles across Ukyo being held captive by a magic-wielding monkey-man, though initially the Lost Boy just says "Screw this, I've gotta find Akane!" After Ukyou convinces him to help, her captor decides to use a magic technique which cripples the victim with depression. Much like Lime's defeat, depressing Ryoga is a very bad idea.
Soun Tendo gets one that overlaps with CMOH. When Kasumi is possessed by the oni that makes you do evil things, he valiantly tries to endure because he couldn't bear to hurt his own daughter (a blow to the head usually gets it to leave), and shows he's a true father when he badassedly tells the thing to take his body instead, and get the hell out of his daughter.
Ranma Saotome keeps it short but epic with a quip in the manga version of the Romeo and Juliet farce:
Ranma: Did you really think sealing me in concrete and burying me in the yard was even going to slow me down?!
In the same vein, as the above Happosai's debut. Before the series, Genma and Soun finally escaped him by getting him drunk on barrels of sake. They then sealed him up in the barrel, chained it up, hurled it into a cave, tossed a sizable bundle of lit dynamite inside with him, then closed up the cave with a massive boulder wrapped in a shimenawa before it exploded. About a decade later, a lightning storm topples a tree and knocks the boulder away, whereupon Happosai heads to Tokyo, none the worse for wear. When Happosai arrives at the Tendo household, Genma and Soun list in terror what they did to him while blubbering it's impossible for him to be there.
Happosai: "You forgot to finish me."note Manga version dialogue / "It's your own fault for not finishing me off."note Anime version dialogue
ANY serious fight between Ranma and Ryoga is chock full of these.
Early on, we learned of Ranma and Ryouga's massive stamina when a "practice" session, in reality Ryouga trying to cripple Ranma and Ranma fighting for his life, lasted all night. Ryouga and Ran a literally fought for hours before Ranma could score a decisive victory.