Kivat often gets a few moments to emphasize the fact that he's not just a fancy belt buckle, but a supporting fighter in his own right. Catching a sword with his teeth stands out as an example.
The debut of each form or weapon usually counts as a crowning moment of awesome.
Even Kido, the owner of Mal d'Amour gets one early on, during Jiro's debut. Claiming to be the ultimate coffee critic, Jiro challenges Kido to make him coffee that he'll consider worth paying for, and Kido steps up to the plate. His verdict?
In particular, he paid 12.5 times the price for it.
The defeat of the Sabbat in episode 8 with a Rider Kick where Kiva is propelled by Castle Dran's fire breath.
Shizuka's drum skills.
Nago stops a speeding car...with his foot.
Wataru gets over his depression and uses DoGaBaKi form to put a beating on a Fangire.
The Kiva and IXA Double Rider Kick in episode 20.
Kengo repeating everyone's order at the dinner party after the waitress gets it wrong.
Riki's first ever busting out of his Dogga form in episode 21 may not be the usual kind of CMoA, but the long wait for it and the Curb-Stomp Battle that followed qualify it as such.
Episode 26. Mio using her Fangire Queen status for the first time to finish off the Spider Fangire at long last.
IXA Rising Form's finishing of one of the Fangires in episode 28. He uses the recoil from the huge blast from his gun to propel himself towards a wall. He then kicks off of the wall and uses the momentum to perform a Rider Kick and destroy the Fangire.
The destruction of episode 33's Fangire. Emperor Kiva uses Dogga Fever to crystallize it before calmly sauntering over to it and smashing it with his hammer.
In episode 35 Dark Kiva summons a snake-like monster in order to test Kiva's power. It succeeds in knocking Wataru out, but Tatsulot brings the newly-repaired Bloody Rose to him and he begins to play it. Somehow understanding the prayer that his father put into it when he crafted it transforms him into a badass dragon creature that proceeds to blow up the snake creature after a short aerial battle.
Kiva's defeat of the shinigami Fangire. He throws the Zanbat Sword and impales it on his own coffin.
King waltzes by Otoya in an attempt to size him up after he discovers his identity. His footsteps leave marks in the ground and catch on fire.
In Nago's fight against Rook he flips in the air and follows through with a sword slash for IXA-calibur. For some reason, a gigantic sun is behind him as he flies through the air.
Wataru's destruction of the giant ship-like enemy summoned by Taiga. After the smaller ones are destroyed he jumps into the air and slashes the larger one in half with the Zanbat sword. After landing he slowly brings the slider on the sword down before the ship finally explodes.
Wataru and Otoya's combo slash against the polar bear Fangire in episode 44.
Nago's declaration that every cell in his body is "burning with justice".
The Movie: Kiva always leaves a Kiva symbol imprint when using his Rider Kick (except in Emperor Form, where Rider Kick is less "kick" and more "repeated foot-blade hacking." Ow!) So in the movie, the fight between a giant-sized monster-Rider and a giant-sized Kiva fused with Castle Doran ends with Kiva slamming the villain into the frigging moon, leaving a massive Kiva symbol imprint. The moon gets better, though.
Heck, the fight itself. After Kamen Rider Arc goes One-Winged Angel and becomes more or less a demon, Kiva assumes Flight Style and continues the fight, leading to a city spanning, dog fight between a dragon and a demon. There are few words than can describe the awesomeness of that fight.