The announcement of Street Fighter IV itself was a Moment of Awesome. Fans and even the Street Fighter team thought that the game would never be made.
ANY fight involving Dudley and Balrog.
Guy gets quite a big one in his ending, where he faces Bison when he's carrying his friend Rose away, threatening with blowing up his aircraft if he doesn't release her. And he succeeds, making Bison back down and saving Rose from his influence.
From The Ties that Bind, we have Sakura bringing Ryu back from the Satsui no Hado via a Cooldown Hug and Ken briefly reaching the State of Nothingness as he fights to rescue Eliza.
Also from the same movie, we have Ryu enter the State of Nothingness against Seth. Prior to this, Seth had been pounding Ryu into the ground and shrugging off everything he threw at him. Ryu enters the State of Nothingness, he burns Seth's arm just by grabbing it before knocking him away and defeating him with the Metsu Hadoken.
Sagat's intro movie has him decide to get a rematch against Adon. Adon is confident he'll win, not knowing he only managed to beat him because Sagat's rage kept him from focusing on the fight. Sagat defeats him immediately with the Tiger Destruction.
Akuma's introduction movie in Super IV: He turns a chunk of a forest into a crater by punching the ground.
As nightmarish as Oni Akuma is, he's undeniably badass. His intro has him obliterate a tree just by exerting his ki, and his ending has him cause and jump out of a volcanic eruption without a scratch on him.