The nature of the games doesn't allow for much of these, but the final boss of Subterranean Animism easily counts. You're fighting a fusion-powered Hell Raven above a respectably huge artificial sun whilst dodging other artificial suns, all accompanied by an incredibly epic Crowning Music of Awesome. Notable in that actually beating her is just as much a CMOA for you as it is for the character you play as.
It's so awesome that the Nico Nico Douga users have created a 3D movie of Reimu's fight against Utsuho, see it here
There are enough example of awesome bosses in the series for its own page.
Cirno's goal is to be the strongest. She's the weakest species in a land of uber-powered gods and monsters. She's the Butt Monkey. Everyone tells her "Not a chance". HOWEVER! Eiki's dialogue in Phantasmagoria of Flower View, and Fairy Wars in general indicates that she's succeeding in becoming, at least, far more than any fairy has ever been. That's right: Screw Destiny; screw what anybody else says; screw reality; and most of all, screw common sense. In a land where the impossible is possible; Cirno strives for Serial Escalation. Keep plugging, Cirno. We're rooting for you.
Another example of this? Take the Extra Stage of Fairy Wars for example, where she manages to defeat Marisa. That's right, one of the most recurring and weakest bosses in the series managed to defeat a main character. Admittedly though Marisa was going easy on Cirno but even she admitted she didn't expect Cirno to be that powerful.
Cirno managing to hold her own against Utsuho in Hisoutensoku, despite the fact that she is starting to melt just from being around Utsuho.
The Touhou Danmaku All-Star Medley. The beginning appears to be a normal stage of Fairy Wars, but then the normal Touhou window layout explodes to the sides and Rumia comes throwing danmaku at you. It features all of the Windows-era characters up to this point, even the ones who don't appear in games. The spellcards are very creative and the widescreen format allows for even more beautiful danmaku to be shown off. Sadly, a playable version will be never released due to copyright issues.
The only characters not in it are Kosuzu, due to FS being released after this, Koakuma, and maybe Daiyousei, due to not being named in the games.
The medley also has various hilarious moments that easily constitute Crowning Moment of Funny such Mokou sprinkling the player with deadly One Ups while making a killer "Full Bomb" item chase them, Nue's spellcard Breaking the Fourth Wallagain by immitating Nico Nico Douga, Kaguya... just helplessly floating in mind air etc etc.
The Touhou Danmaku All-Star Medley creator also made Unreasonable Mechanism, a ridiculously hard game where you have no lives or bombs. You have to clear the entire thing without dying once, or you're forced to start over. The player (the creator's friend, presumably given no help) is forced to deal with the title text falling on him, fairies that have Master Spark and turn into homing versions of Utsuho's giant bullets, instant death when timing out boss attacks, stalking killer 1UPs, and so much more. When Marisa comes from below and rams into him after he clears the stage section for the first time, you can see the player banging on the keyboard in frustration. After suffering 220 deaths, he manages to pull off a completely perfect run which makes this an incredible Crowning Moment Of Awesome.
Another meta example: ZUN coming to AWA 2013 as a Guest of Honor—his first time coming to the United States as a convention special guest. This made a lot of Western Touhou fans happy, with many coming to AWA because of him. You can read a transcript of his panel here; he, among other things, expresses surprise at the large number of Western fans and acknowledges his fans, including those who create fan remixes of his music.
The panel also features a Funny Moment regarding ZUN and his experience with alcohol in the U.S.:
Q: During your stay in America, have you tried any new interesting beers? ZUN: Iíve tried many beers. Many interesting beers; however, I learned one thing when I came to America. Meals are too big and beer is too little.
There is also this gem that shows just how Genre Savvy ZUN is about the fanbase:
Q: Have you ever considered taking some of your musical ideas and take them into orchestras, small bands, group ensembles, and etc? ZUN: I donít need to, because I have the fans do it for me.
And this one:
Q: Do you have any advice towards any aspiring game designers? ZUN: Itís a simple answer. JUST DO IT.
The final battle of Hata no Kokoro's story mode in Hopeless Masquerade, where Kokoro fights Reimu, Byakuren and Miko all at once. The only thing more badass than that matchup is the fact that she wins.
Meta-wise, because you could play as Kokoro before the proper patch for her came out, it mend that the player could play through the entire story (and fighting off Reimu, Byakuren, and Miko) with no specials or spell cards.
While we're on the topic of fighting games, Komachi's fight against Tenshi in her Story Mode definitely qualifies. She gets so pissed at the Celestial for abusing the cycle of death and rebirth that she breaks her carefree facade and completely demolishes her. And unlike most of Tenshi's fights, she never returns to pay back the beating in her story mode, suggesting that she was already going all-out the first time around and got beaten cleanly.
Sanae's final battle in Hisoutensoku against Suwako due to the incredibly creative uses of the later's abilities including causing he nuclear reactor they are in to erupt and battle using lava frogs. This culminates in a freefall battle between the two
Seija Kijin is not the most powerful youkai ever. She's not even a stage 6 boss. She is however clever, and very creative as proven by her being the Stage 5 boss. She doesn't have that high a bullet count, but she makes every bullet count as she peppers you from the top, bottom, and the mind by reversing your controls. In Gensokyo where power seems to be the key to every solution Seija manages to prove that boring is practical.
What's even more impressive is that she goes on to take on half of Gensokyo by herself, and none of them are holding back. Through clever usage of several cheat items, she gets to beat every single one of them, up to and including powerhouses like Yukari, Byakuren, and Miko.