Any time Ryu lands the Shin/Metsu Shoryuken. The game freezes and the opponent vibrates for about 1-3 seconds after each blow. Just seeing it in action gives you an idea of how obscenely powerful and painful the move really is. It's not hard to imagine how Sagat got that scar.
This is quite possibly one of the most awesome fights ever fought in Street Fighter III (here's a lower quality version of the whole match).
For people not familiar with SF3, here is a quick briefing: Ken (the dude, played here by the legendary Daigo Umehara) has very little health at the beginning and it drops to nigh zero after a few seconds. Then Chun-Li (the girl, played by Justin Wong) starts her super attack, kicking the opponent about a dozen and a half times in a very close succession. The rules are simple: if Ken gets hit at all, even blocking, he loses. What he does is parry every single one of her eighteen lightning fast attacks (which, by itself, is nearly impossible - he has to press forward just as she strikes, and the timing is ridiculously unforgiving) and jumps just before the last one so he is in position to start his ownsuper attack and take her down for the win. The crowd went absolutely wild.
The timing actually isn't that unforgiving. The awesomeness actually comes from the emotional aspect of a complete situation reversal: When Chun Li gets in a kick at 0:21 of the 57 second clip, everyone suspects the match is essentially over. Ken has no health, and so the next blow Chun Li deals will kill Ken, even if Ken blocks (because blocking reduces damage, but does not completely negate it, and Ken is at such a low health level, that even the reduced damage would be enough to kill him). Then, at 0:27, we see the tell-tale blue flash of a super. This is where you expect the match to end with Chun Li winning. Ken parries the first blow (parrying completely negates damage to 0). Okay, fine, parrying the first blow is pretty easy, and you figure it's a desperation move, because really, Ken has no other options, but he's just delaying the inevitable. Ken parries the next blow, and the one after that. Wow, the guy playing Ken is pretty good. And the next, and the next. This is when it finally sinks into your mind that Ken might actually be able to go all the way (this when you hear the cheering suddenly jump up really loud). He just keeps parrying and parrying. When he parries the final blow in the air at 0:32, your heart is racing, because he actually managed to parry the whole attack sequence. Ken survived. That was unthinkable. He did it. But this is only the beginning. Ken then lands with two kicks, follow by his own blue flash, indicating that he is starting his super. And when this happens, your eyes suddenly dart up to check Chun Li's life bar. Could it be? Is it possible that Ken might actually kill Chun Li with this super? And indeed, her health bar is around 5%, and the super connected. That's it. Chun Li is dead. Ken did it. It is with this realization that the roar of the crowd transforms into a feverish pitch.
What adds to the defeat, is that if you notice the score above the life meters, Ken has about 28,000 points when the video starts, while Chun-Li has 100,000. The cool part is that with all the technicals, combo kicks, and the Super finish that Ken performed, the final score is Chun-Li:107,000 ; Ken:107,500
Along a similar vein, this. Not only did he parry the move, he did a 720 motion in the middle of it. Sweet.
Most every ending of Alpha 3 gives your character a chance at a Crowning Moment of Awesome. Unfortunately, most of them aren't canon, but that doesn't really detract from watching E. Honda defeat Bison with one Sumo Torpedo or watching Charlie kill Bison twice, then shoot him down in his plane and nuke him when he still won't die after that.
The best example is Zangief destroying Bison's power source by repeatedly piledriving E. Honda into it.
Street Fighter IV features Gouken, and he demonstrates how powerful he really is now with his "Power of Nothingness" in his and Akuma's endings by firstly, taking Ryu's Shinkuu Hadouken with no damage and not even blocking, and secondly, stopping the Raging Demon dead in its tracks without even moving with his back turned. Dodging and surviving the Shun Goku Satsu is one thing, but Gouken stopped it without even moving. With his back turned.
Gen did nearly the same thing and at least a year earlier to boot. The officially stated trick to beating the Shun Goku Satsu is emptying one's mind of all thoughts and feelings. Granted, this is still something only absolute masters can do, people in the realm of power Gen, Gouken and Oro occupy.
More of a crowning moment of awesome for all of fighting games, but without Street Fighter, it would have never existed. Ode to the 2-Hit Combo is a magnificent, heartfelt love letter to the entire genre and all of its fans, and turned a combo video into a work of art.
After Bison is revived and blasts Guile with lightning.
Guile: What happened to the purity of unarmed combat?
Bison: This is merely Superconductor Electromagnetism. Surely you've heard of it. It levitates bullet trains from Tokyo to Osaka. It levitates my desk, from which I ride the saddle of the world. And it levitates... me.
The scene in the Manga in which Vega attempts to kill the dark hadou possessed Ryu and Adon, along with Sodom, Cammy, and Chun-Li. All hope seems lost, then suddenly a Shadaloo officer strikes the Spanish assassin before he can press the button to kill them. The officer is revealed to be Guy who disguised himself as a Shadaloo soldier to fight Bison, but revealed himself to save their lives. He makes quick work of Vega, then stops Evil Ryu from killing Adon by kicking several oil drums at him Final Fight style. Then Guy faces off against Ryu, blocking and countering every punch from his Shun Goku Satsu while urging him to control his killing intent before landing one final blow to Ryu's face that knocks him out, subduing him and returning him to regular Ryu.
Sakura standing up to Bison, even before she's into the whole "street fighting" business. Sure, she's but a noisy fly to him at that point, but that sort of thing takes guts.
Ryu defeating Bison and destroying his VTOL with his Shin Tatsumaki Senpuukyaku and then finishing the job with a Shin Shoryuken that wouldn't have been out of place in Dragon Ball Z.
Nearly every part of the final battle between Ryu and Bison is like something out of Dragon Ball Z. Each of Ryu's Hadoken's, and tasumaki senpukyaku's are turned up to eleven
Ryu Final: Street Fighter III:
Ken defeating Gill purely on account of the love for his family, at which point Ken stops being a warrior for fun, glory, or for the sake of fighting, and Ryu can't even compare to him anymore.
Ryu's awakening to the Fist of Wind during his match with Dudley.
The entirety of the Whole Episode Flashback to the aftermath of Sagat's original defeat at Ryu's hands. Especially him palming a falling tree (and leaving deep gauges on its bark with his fingertips) to keep it from crushing a child, and blocking a hail of bullets with his hand.
Ryu and Sagat's final rematch. If Oro was astonished, and Sagat's scar bled again in joy, what else is there to say?
Ryu figuring out the Shun Goku Satsu, surviving it, AND countering it all while being on the receiving end despite a broken right arm, a broken left hand, and a broken leg.
Sakura figuring out how to do the Hadoken within hours of having it explained, and never having trained for it. Even Dan is terrified at the kid's potential.
Karin graciously acknowledging Sakura as her perennial, but friendly, rival. Which is quite a change considering the Udon comics went the "enemies" route.
Speaking of Karin, her "bonus feature" manga at the end of each book has at least one per issue, culminating in her falling from an airplane and using a security rope (which she was using to fight while on top of the airplane... long story) to wrap around a bridge and land perfectly safely, merely ripping a streetlight from the asphalt in the process. Remember: In Everything, Be Victorious!
Master assassin Gen undergoing a Heel Realization and a Heel-Face Turn in the span of a few seconds merely because a leaf from a sakura tree blocked his deadly Zan-ei from directly striking Sakura herself. A leaf. Even his eyes, previously angry and black as pitch, returned to a kindly, human appearance afterwards.
Zangief, defeated and battered beyond belief by Sakura and Cammy's combined assault, refuses to fall over because his body is as much his Russian comrades' as it is his, and he cannot, will NOT, let it fall. So he throws his hands in the air and goes into his victory pose, and remains standing as he falls unconscious.
Sakura finally meets Ryu after chasing him all over the globe, and the first thing she does is challenge him to a fight. Doubles as a Heartwarming Moment.
From the UDON comics, the battles of Ryu and Ken versus the Shadaloo thugs at Ken's wedding and Chun-Li, Fei-Long, and Gen versus the triad led by Jianyu and Xiayu are especially memorable. But probably the best is Charlie, who was seemingly killed, fighting Bison while also charged with Psycho power.
During the tournament, Vega is defeating Ken, and then steals from his pocket a letter from Eliza. Mockingly, Vega reads it out loud "It's a boy". This gives Ken the Heroic Resolve to get back on his feet and hit Vega with a Shinryuken.