In the manga, Train has one of these when, after realizing he was tricked by Sephiria into going to Creed's castle to save Rinslet, deliberately doesn't help the Chronos numbers fight Creed. So not only did he manage to save Rinslet in a dramatic fashion, he managed to (temporarily, at least) avoid getting involved with the fight between Creed and Chronos, confuse the hell out of the Apostles, AND depress Creed (to the point where Creed lets himself get hit by Beluga out of sheer shock and sadness).
I have got to say running away has never looked so badass.
Another moment in the manga is when Creed is about to shoot Sven with a nanotech "Lucifer" bullet, and Train takes the bullet for Sven in his arm. Train promptly punches Creed. Hard. The awesomeness of this lies in how calm Train is about the whole thing - especially when everyone else (especially Creed) is panicking.
Happens in the anime, too, but it's less impressive because there are other things going on at the time, and Sven is replaced by Kyoko, and Creed is replaced by Doctor.
When Naizer (a.k.a. Number V) faced off a "Lucifer" powered werewolf, the werewolf just keeps on regenerating, making it virtually invincible. Naizer however managed to obliterate his opponent by attacking the werewolf in all places at a speed faster than the nanomachines can regenerate it. The end result is literally a pile of dust. For a character who only gets minimal appearance time, Naizer is an incredibly Badass character.
Train, in order to prove how worthless Shiki's Tao is, uses up his last Railgun shot AND takes Shiki's strongest attack, and still manages to defeat Shiki in one blow effortlessly.
Eve got one from her fight against Leon. Pinned underwater due to Leon's manipulating the air overhead in a destructive manner, she transforms herself into a mermaid complete with bikini to give her the extra push from the water to get to him. Oh and she then slapped him silly with said tail.
Eve also gets one whenever she uses her hair as a weapon (transforming it into, usually, a large blunt implement)
Let's face it, Eve is a walking Crowning Moment of Awesome all on her own. But on the subject of Leon, this troper was most impressed by her tanking Leon's Death Twister by turning her entire body into steel.
One rather rare crowning awesome moment that is found anime-only: When Train, while still in Chronos, is assigned to break into Torneo's mansion and eliminate Eve, he manages to break through the guards and defenses so fast it looks like a hurricane swept through the place. Coupled by how Sven and Rinslet arrived earlier than him and were running at full speed, yet were completely incapable of passing him (despite the fact that he's actually hindered because he's the one taking care of all the guards and security cameras and opening doors to find Eve). The smooth animation and quickness of his actions definitely helped it become an awe-inducing moment.
Yeah that part was awesome. He just shoves the door open, looks left and right while pointing his gun, leaves the room and repeats it for every damn room in the hallway.
Another anime-exclusive moment. Preta Ghoul makes a return appearance among the Apostles of the Stars near the end of the series, attacking one of the mauve shirt sweepers in a crazed frenzy. While Train runs off to deal with Creed, Sven and Eve jump to the girl's defense. Ghoul's corrosive ki makes him impervious to bullets and touching him or being touched by him is rather lethal, so it looks like our heroes are in a bit of a bind. But Sven notices that Ghoul's shirt doesn't melt off of him despite being in constant contact with his body and aura, so while Eve distracts Ghoul by taking the form of Saya Minatsuki, Sven relieves Ghoul of his shirt via fishing pole, wraps it around his fists, triggers the vision eye, and goes toe-to-toe with Ghoul in an impromptu boxing match with Eve as the bell (literally; she grew a boxing-ring bell on her head like a hat and turned the end of her hair into a mallet to hit it with).
Anime-only example: Train's assassination of Lib in the beginning. Again, the graceful animation, and just how freaking fast Train is in comparison to Sven makes it a crowning moment of awesome for Train. Not to mention that, considering that Lib was an annoying, ugly man that viewers undoubtedly don't care about, it's refreshing to see Train do him in.
Sven unveiling his magical eyeball. Both the first time and as the "upgraded" version that lets him dodge pretty much everything.
Beluga's Heroic Sacrifice is this and a Tear Jerker. The guy holds up the entire ceiling while Jenos and Nizer get out, talking the entire time about how he's glad he didn't have to kill one of his friends.
The last two battles between Creed and Saphira and Train and Creed. Badass swordfight followed by badass sword vs gun fight? Awesome. Seeing two different people (one of them a girl) stand up to the godmoding Creed? Awesome. Sephira's final attack and repeated defeats of Creed? Awesome. Creed's One-Winged Angel moment? Creepy, but awesome. Train whipping out another railgun and somehow, not making it feel like an Ass Pull? Awesome. And the look on Creed's face when he realises he's lost? Absolutely, freaking priceless. It's an amazing wrap-up for a better than average Shonen series.
Shao Lee (Chrono Number X) gets a brief one in Creed's castle. When Jenos and he are taking on two of the 5 super soldiers Echidna has sent after them, Jenos finishes his off, then walks over to see how Shao did. He finds Shao standing there with his target missing several limbs and his head on the ground, while Shao himself is completely unharmed (considerable, given the fact that even Sven, Eve, and Jenos were given some difficulty against the soldiers). And to make it all the more epic, the fight ends with the soldier claiming he is invincible, and Shao responding "Maybe you are; against someone else." before shredding him.
Also worth considering is that Shao's weapon is basically a razor-sharp bedsheet made from Un Obtanium. It's very pretty. The fact that Shao can make that weapon look awesome is, in itself, awesome.