Mai-HiME/Awesome

Anime

 * Haruka Suzushiro, a Badass Normal girl in a cast of super-powered girls, permanently won a spot in my heart when she managed to headbutt Shizuru right before disappearing. The instant Haruka got back up on her feet and shouted "You!", stomping angrily toward her with life sparks flying everywhere...well, it's pretty much a given that something cool was about to happen.
 * That's not her only moment, though. It takes enormous brass (and, uh... muscle) for someone to stand up to a group of fully-armed soldiers and repeatedly kick one of their tanks...and walk away from it without hurting her foot. Even the students were going, "Holy crap!"
 * Pretty much all of Midori's first battle where she showed off her HiME powers.
 * Oh, let's give the main Power Trio their credit, too. The cake-hungry Mikoto chases an Orphan away from her cupboard in the Cooking Duel episode, and she and the other two girls track it to a secluded area, where they all combine their HiME powers (Mikoto first, then Natsuki, and finally Mai) to pound the crap out of it before it can land a blow. Sweet. (Of course, Mikoto never did get her cake. ;_; Although considering the judges of that Cooking Duel ended up literally hospitalized, maybe it's best she didn't get it after all.)
 * Did we mention the part in the first episode where Mikoto split a friggin' cruise liner in half?
 * Natsuki's Big Damn Heroes moment in Episode 14. Shooting the guns away from a handful of armed soldiers, blasting them with a flash cartridge and then going all River Tam on them? Priceless.
 * Natsuki's decision to sacrifice herself in order to defeat  Her speech before she tells Duran to load his silver cartridge is both unexpected and moving.
 * Mai's greatest moment comes at the end of the big battle with Searrs, in which she and Kagutsuchi fly straight into a Kill Sat's beam, and not only succeed in blocking it but keep going up into space to take out the satellite itself. Oh, and we can't forget that the process involved getting disintegrated, and resurrecting anyway.
 * One of the most powerful moments involving Mai is in episode 3, when she accepts Kagutsuchi, and ends up being frightened out of her wits at what she's just done.
 * Shizuru gets one of her own when, in her first battle with Nao, she bests her without breaking a sweat, and leaving half the cliffside sliding into the sea after one stroke of her naginata.
 * After spending a good deal of the series as a combination of The Scrappy and The Load, Tate proves himself a Badass Normal in the finale, taking on the all-powerful Obsidian Lord with just his kendo skills (and this immediately after ).
 * Actually, Tate's greatest CMOA happened

Manga

 * Akane summoning her Child and curb stomping the Three Scale Sisters to save Mikoto and Kazuya.
 * Natsuki freezing the shells shot at her and Yuuichi, then shooting off her Princess earring and defeating her while she's in the middle of taunting her.