Allen standing up to Kevin, which is so awesome, in fact, that he nullifies Shion's Face-Heel Turn. Even more so, given that he defeats one of the most powerful characters in the series by *being beaten up.* Um... just watch it and it'll make sense.
Even better: In the ending sequence Allen, a character who it must be said, has no special abilities or combat training save for one moment when he's a Guest Party Member, tackles a Gnosis, beats it with an assault rifle and then shoots it dead at point blank range. Even the characters were shocked.
How about when the Dämmerung and her little BFG fleet come to the rescue as both the Kukai Foundation and the Federation fleet are about to be overrun by the Gnosis, back in Episode I? It's complete with Mitsuda's very own take on Ride of the Valkyries.
Jin gets one in Episode II, during his battle with Marguilis. In Episode III, his CMOA is also a Tear Jerker and an Ending spoiler
Many gamers and even Game Informer Magazine considered Albedo's little...moment with MOMO to be awesome.
Her first in was Episode 1 when Shion was captured by a Gnosis and was on about to be killed when Kos-Mos shot it in the arm freeing Shion with a wall between the two, fires a couple of rounds at the Gnosis though ineffective, activates the Hilbert Effect, which is kind of like Kryptonite to Gnosis making every last one in the battlefield solid and killable, and destroys that one pesky Gnosis and any other ones that came after her.
Albedo's (in)famous scene from Episode 1. It's scary for some, but that scene in particular permanently solidified him as an Ax-CrazyEvil Albino.
When KOS-MOS defies Wilhelm. "I am not Mary. I am... KOS-MOS!"
Many players had their own personal CMoA's once they taught their party the Short Double, Short Revenge, and Short Counter abilities. Dodging dangerous hits from bosses, then retaliating with crit damage, sometimes twice, can make one fist-pump the air in triumph.
Chaos destroying a Gnosis with a single touch, and his arrival surprised KOS-MOS, who immediately checks her video memory and gives us the first hint that he's not normal. Too bad he's pretty much a bystander for the rest of the games.
Jin's Heroic Sacrifice decision at the end of episode III when he goes back to help KOS-MOS fend off the Gnosis. He roars into battle with his ES, Asher, before going on foot and slaying Gnosis with his katana. One Gnosis stabs him through the shoulder with its sword, but then Jin pulls it out and uses it to fight other Gnosis.