Layton gets at least one of these in every game in the series. That's why he's part of the Pantheon.
At the very end of Curious Village, after Layton and Luke discover that Flora, Baron Reinhold's daughter, is the "Golden Apple", Layton's arch-enemy Don Paolo shows up in a massive flying machine and starts destroying the tower. The group then attempts to flee the tower...but the stairs break, allowing Luke to escape, but not Layton or Flora. Unfazed, Layton returns to Flora's room and builds a makeshift glider out of parts of a huge globe and some curtains. With the tower collapsing around them, Layton and Flora glide to safety. Layton's triumph of intelligence over brute force make this scene symbolic of the entire game. The fact that 90% of the scene was animated didn't hurt matters.
Although the most awesome part of that scene was either the part where Layton destroyed Don Paolo's machine by accident or the part where Don Paolo had these weird bommeknockers just flying into the tower. At least, in my opinion.
Alternately, when Layton solves the game's first puzzle after glancing at it for a few seconds (admittedly, said puzzle was a bit of a pushover, but still...).
Also alternately, a scene near the end of the game where Layton is summoned to Reinhold Manor by Inspector Chelmey. After arriving, Chelmey gathers everyone in the manor together for a giant meeting, and then loudly and insistently accuses Layton of the murder that happened earlier. Even though Chelmey correctly declares that Layton's alibi is incredibly weak due to Luke being the only person with him (and he could have easily been in on it,) Layton is completely unfazed at the thought of the inspector pinning the murder on him in front of everyone. Instead, he calmly identifies Chelmey as an impostor, delivers an incredibly long recap of every single mistake and contradiction he noticed since the very beginning of the game that all points to this conclusion, and even successfully traps him in a Bluff the Impostor name drop in one of the many pieces of evidence he brings up just for extra good measure, leaving Don Paolo with no choice but to drop the disguise. It's just staggering how thoroughly Layton destroys Paolo with mountain after mountain of logic in this scene.
It was pretty cool when the aforementioned stairs fall underneath Luke, and he manages to jump across as it crumbles, but she thinks that if the ending doesn't, the scene where Layton performs a diving save to stop Luke from being crushed by the Ferris Wheel takes the cake.
The music for the whole ferris wheel scene even made it better. Not to mention the part where the ferris wheel rams into a mysterious shack and flies into the lake in slow motion. Layton. Is. AWESOME!
As Layton and Luke climb the tower Layton reveals what was going on with almost all of the mysteries. This is the first time that we see that he doesn't just solve puzzles: he solves mysteries. We actually see that he HAS been figuring everything out this whole time.
And then, of course, there's the ending to Diabolical Box ... you can see from the choreography that Layton doesn't go into the Sword Fight knowing how to fence, meaning that he has to FIGURE OUT HOW ... and he DOES, becoming more and more skilled as the fight goes on until he finally hands Anton's ass to him. Absolute. WIN.
Actually, if you read his profile in the game, it tells us the Professor has been taking fencing classes. Doesn't make it any less awesome, as classes are a world of difference from actually having to fight for your life.
The events of "Miracle Mask" make it clear that Layton was a fairly good swordsmen in his youth, though gave it up after his fencing partner's apparent tragic death. The fact that he's able to rekindle his ability after years out of practice, to save his friends, is awesome itself.
Unwound Future, where the CMOAs just keep coming one after another. How about watching him speed off in the Laytonmobile and driving it off the edge of a hill in order to successfully land on the Big Bad's Humongous Mecha?
He also gets one in his conversation with Celeste just before this takes place. He urges her to get out of the area because it's dangerous, and when she asks what he's going to do, his response is very perfectly Papa Wolf. He doesn't say "I have to stop (the villain)," or "I'm going to save the city." He says, "I'm going after Flora," whom the Big Bad has abducted. And when Celeste replies that he's crazy and he could be killed, he doesn't even dignify that with a response.
Don't forget the scene earlier in the game when he spontaneously builds a machine gun — out of a slot machine! Did we mention he's under fire when he does this?
Luke tries for one when Future Luke drags Flora out of the restaurant; he valiantly leaps to stop the incident but is unsuccessful. The effort was still a little CMOA though.
Luke and Flora share one toward the end of the game. After Layton frees her from the holding cell where she was placed after her abduction, he tells the pair of them to go and wait for him by the car in relative safety. They both refuse to leave him, insisting that they won't let him go charging into danger alone.
Don Paolo doing such a convincing impression of the Professor that it fools Luke and Flora.
Eternal Diva (the movie)
The Sword Fight between Layton and Descole. Descole has a real sword. Layton has a lead pipe.
Luke actually has one when he convinces the Professor to let him save Jenis. Which he does. After Layton drives his mini-chopper in the way of a drill headed straight for Jenis and Luke, and, of course, survives.
To say nothing of the spectacular flight to the castle. With Scenery Porn galore!
The moment where everyone in the party decides to sacrifice their lives to deactivate the Azran Sanctuary. The first to decide is Luke. He's only 10 years old, but he willingly steps onto the pedestal to save the world even knowing that he'll die. Bronev also decides to make amends for what he's done by activating the final pedestal.
Thankfully, nobody dies for good, thanks to Aurora, but it was still a gripping scene.
After all his hard work, Grosky finally gets a promotion at the end of the game. The man handing out the medals has to stand on his tip-toes to reach Grosky's manly pecs. You can even see Chelmey applauding in the background.
Miscellaneous unsorted moments
The sword fight with Anton. He sure has energy in him for someone who's at least 80.
There's also the sword fight with Descole. Descole has a real sword. Layton has a lead pipe. Did I mention that they're fighting on top of a mobile fortress, too?
Clive has one through all of Unwound Future. By Crazy Awesome he's managed to build a giant, murderous mecha underneath an unseen but mentioned Elaborate Underground Base (presumably filled with more than enough kidnapped scientists) underneath an entire fake-future London (with hundreds of kidnapped citizens) that's built under the real London. Remember: throughout all of the game, there's one thing you never see: the cave walls around "future" London.
Any time that the Professor Macgyvers an object out of whatever he's got lying around, especially impressive because it tends to happen under quite stressful circumstances, but Layton stays cool through all of them.
Every accusation scene.
If you managed to solve a hard puzzle without consulting the Internet, you deserve a pat on the back.
Not an in-universe one, but in one of the special episodes in Inazuma Eleven GO Chrono Stone, the fifth entry in a very successful and popular soccer RPG by the creators of theProfessor Laytongames, Layton, along with Luke and Emmy, perform a hissatsu shoot (read: magical soccer technique) called Triangle ZZ together. That's a 35-year-old, kicking a ball, sending it blasting through the sky towards the goal enveloped in a red aura.