Troy and Gabriella singing 'Breaking Free' in front of the whole school at the end of the first film. Especially when they get everybody dancing with them.
The very fact that both of them - a Shrinking Violet whose at a brand new school and a star basketballer under huge pressure with students and teachers watching his every move - had the guts to audition for a musical against experienced performers. Anyone's whose been to high school can tell you that would be terrifying.
To elaborate on the former: previously, Sharpay had always been the bad girl trying to win the lead role, always backstabbing, manipulating, and buying her way to the top. Whenever Troy and Gabriella beat her out, she'd put a smile on her face and plot for next time. But in this movie, Tiara crushed her. In one sweeping stroke, she replaced Sharpay as the villain, humiliated her, burned her acting, stole her costume, revealed that all along she'd been playing Sharpay for the fool and then, turns the light off on her dresser door. Sharpay completely breaks down. Then, for the first time in the whole series, she decides she's not going to sit there and whine when she doesn't get her way. She takes the challenge face to face, puts on her spare costume, and, in what could be considered the series' only fight scene, SHARPAY UPSTAGES HER!!! This is not only her CMOA, but her turning point from Villain to Hero.
High School Musical:
Kelsi: Pianist here Ms. Darbus. Sharpay: (menacingly) You really don't want to do that. Kelsi: Oh yes, I really do. Sharpay: (Shocked exclamation and falls back in line)
Followed by Ms. Darbus'
Ms. D: Now THAT'S show biz.
The ending scene after the credits where Zeke's cookies are so amazing that Sharpay falls in love with him.
This was a deleted scene, but apparently Ms. D and Coach Bolton were supposed to have a musical face-off in the Principal's office. That would have been a sight to see, especially since Alyson Reed (Ms. Darbus) formerly played Cassie in A Chorus Line. On Broadway. The woman has pipes, folks.
High School Musical two:
Ryan vs. Chad in a musical baseball game.
Ryan: You don't think dancing takes some game?
The fact that Ryan as actually really good at baseball, to the point of impressing Chad.
Also, when Troy finds Ryan with Gabriella by the pool and Ryan makes a comment about the brownies Gabriella's mom makes? Troy shuts him down hard.
Ryan: Her mom, makes the best brow— Troy: I know, I've had them.
Also, Gabriella's confrontation with Sharpay.
Ryan standing up to his sister and making the East High Gang's participation possible deserves a mention. Not only is he awesome at what he does, he also finally graduated from being Sharpay's lapdog.
High School Musical 3: Senior Year:
Troy's song scream where he DANCES ON THE WALLS AND CEILING!!! That whole song in itself is a CMOA. It even doubles as Crowning Music of Awesome.
"The Boys Are Back" wherein they use metal bars as samurai swords and hang with what looks like guerrilla break-dancers.
Also, when mini-Troy and mini-Chad dance.
Speaking of upstaging: Rocketman is introduced as the annoying fanboy of fail, and, when told he actually has to go onstage as Troy in the musical, goes into shock (his best friend suspects he stopped breathing). After freaking out some more in his dressing room and missing his cue entirely, he rocks onstage, completely steals the scene from Sharpay, actually turns out to be a good singer in his own right, and gets an in-universe standing ovation. The best thing: he completely ignored stage instructions and the costume department, threw on whatever he could find and had fun. He basically improvised, aside from the song. And it is the single most badass and hilarious moment in the entire franchise. Try watching that part of the scene without immediately laughing and saying, "that was just awesome, good for him." Watch it for yourself.
Ms Darbus' conversation with Troy post-"Scream", wherein she proves she truly does understand the spirit of theatre and isn't just a poseur after all.
The titular musical is choreographed in its entirety by Ryan. That's right, the guy who was Sharpay's shadow for one and a half movies is so good at what he does that he's put in charge of an entire musical and the results are amazing! He even created a dance for Chad and the guys with basketballs, one number which is reminicent of Broadway, and then he managed to make Jason look good on stage. The Juilliard people were so impressed they said "screw it" to the "one scholarship" thing and just gave him another one.