Might be primarily a Tear Jerker or Nightmare Fuel, but Norman trying to talk to Aggie by telling her her story and doing it even as she throws everything she can at him was pretty cool, especially with the music playing.
The confrontation with Agatha was awesome in a dozen different ways. Eerie, disturbing whispers when he asks her how sleepy she is, razor spikes from the ground, and lightning. So much lightning. ALL OF THE LIGHTNING. Then the world starts to tear apart into a giant abyss. And Norman manages to keep reaching out to the poor girl, the entire time, somehow not dying.
Arguably for the writers, as this is the first time an American family movie has a character who's gay, has a boyfriend, and isn't stereotypically macho or campy:
Mitch: You're gonna love my boyfriend. He's a total chick-flick nut.
Neil provided some subtle moments of awesomeness. Not only is he awesome for being so upbeat and trying to be friends with Norman, but when Norman's being messed with by a creepy old man and chased by a bully, he doesn’t hesitate to step up and try to get the bad guys to back off. Kid's got a pair of brass ones.
No kidding! Little guy's first reaction to a zombie trying to grab Norman through the top of a moving van? Grab the undead corpse and try to physically restrain it.
ParaNorman is what happens when the truly epic stop-motion animators from Coraline work in ideal conditions.
Uncle Prenderghast gets one when he dies... and promptly forces his ghost back into his body, declaring, "Not yet. Not yet!", followed by a mad cackle. He may be a lunatic, but he's an awesome lunatic. (Sure, he dies for real a second later, but hey, can't fault a guy for trying. And even managing it for a second is pretty impressive!)