The reveal of Andy Dufresne's escape, one of the most heartwarming stories on film despite its subject matter, provoked unfettered joy at his triumph.
Seconded, especially if you include Norton getting busted as part of the same moment. (And it's fairly reasonable, as they result from the same thing.
In particular was that moment when, mid tantrum, the warden inadvertently threw a pebble through the poster of Raquel Welch and discovered the tunnel. The slow realization of all the guards there of just how thoroughly they had all been played was Epic.
There's also the rooftop scene, with awesomeness coming from Andy and Captain Hadley with every line. "Sir, do you trust your wife?"
Not to mention the scene where Andy plays "The Marriage of Figaro" over the prison's loudspeakers, and he's sitting back in the locked office when the Warden comes up to the door and orders him to turn it off. Andy reaches over to the record player — then smiles slowly and turns the volume up.
Andy doesn't have a monopoly on awesome. Red has one when he lectured the board who would determine his parole. The board in turn decide to be awesome by releasing him because of this.
That, or they just figured he sounded more sincere this time around.
It was a different (and probably less biased) group of people than the previous parole hearings, although presumably they did think he sounded sincere.
What makes it awesome is that, in a sense, Red demonstrates an understanding of the seriousness of his crimes, that you can't take back what you've done, and that a single bad decision as a young man can put you in prison until you're old. In doing so, he shows what he's learned better than by simply talking about how he's changed.
The shot of Andy emerging from the sewer, running through the rain and standing with his arms in the air. Pure Brilliance.
It is also the first time in the entire movie that Andy shows unbridled joy as he laughs in the rain. The audience most definitely shares this sentiment.
The music is just fantastic. That set over Norton's threat to cast Andy "down with the sodomites" makes it all the more chilling, and is used to perfect effect to convince the audience that Andy's been pushed over the edge, making the ending the crowning moment it is.
The little extra when the Warden is caught out. He rushes to his safe, and finds that the night before Andy put his copy of the Bible in instead of the log books. Even better, he left a note in the front 'You were right warden, salvation lay within', an Ironic Echo to something the warden had told him, and, as if there needed to be any more, the rock hammer was hidden so that when you opened it, the Warden opened it up to 'Exodus.' Bad. Ass.
When Andy talks the guys who are beating him up out of raping him using his knowledge of medical trivia.
Especially since he has the utter nerve to sass them, even while facing a potentially excruciating death:
Boggs: Where'd you get this shit?
Andy: I read it. You know how to read, you ignorant fuck?
Hadley may be an unpleasant asshole, but when he beats seven shades of blue out of Boggs, you can't help but cheer for him.