Alan and Van Pelt's final faceoff, where Alan not only doesn't run from Van Pelt, but stands up to him. It's enough to make Van Pelt finally show Alan a modicum of respect in spite of everything.
Van Pelt: End of the line, Sonny Jim. Game's up. Start running. Alan:[pause] No. Van Pelt: Aren't you afraid? Alan:[nonchalantly] I'm terrified. But my father says you should always face what you're afraid of. Van Pelt:(laughing) Good lad! You're finally acting like a man. [raises gun] Any last words? [Alan looks down and notices his game piece moving to the end of the board, after which the word "Jumanji" appears.] Alan: ...Jumanji. Van Pelt: Huh? Alan: JUMANJI!
Also, Alan got trapped in the jungle of Jumanji as a kid. Sarah stopped playing the game and thus Alan remained trapped for twenty-six years. And he survived. Most kids probably wouldn't last a few days or weeks in such a situation, but Alan adapted and proved himself a survivor.
The scene in where he finally got released; and by "release", "hitchiked" with a fierce lion manifested by the game would be more concise. Adult Alan stood his ground, with nothing but a dagger between himself and the carnivorous feline, as it imposes over to him and eventually tricked and trapped the beast in Aunt Nora's bedroom. And through no small part the riveting background music made the spectacle iconic.
A small one, but in the prologue, when speaking with Alan, Carl shows his ground-breaking invention: Parrish Sneakers. While the concept of trainers may not be new (since they were invented in the late 1800s), this style looks like a time traveler dropped them off from the '90s. And this is the 1969 mind you! Carl wasn't exaggerating when he claimed these were the future.
Alan busting out his ancestor's Civil War saber to deal with the plants. "Sorry, Angus. Harvest time!"
Possibly when Judy tells Aunt Nora that she didn't lie when she found out the only reason they were able to get the house dirt cheap was because the rumored murder of Alan Parrish took place in the house.
Aunt Nora: Okay, that's it. I am sick and tired of your lies, young lady. You're grounded.
Judy: Fine. There's nowhere to go in this stupid town, anyway. But just for your information: That wasn't a lie.
Her greatest moment comes when she is shot in the neck with poisonous barbs. She, a twelve year old CHILD spends about five seconds processing what has happened and the fact that she will almost surely die, before calmly pulling out the barbs, telling her brother "I'm fine, help them." Then bringing the game board over to Alan so he can roll his turn without a word of complaint. Nerves of Steel doesn't even BEGIN to cover it.
For a kid that was afraid of just talking, Peter goes through leaps and bounds of bravery, hanging upside down from a branch to get the game, creating a makeshift rocket launcher, and fighting off spiders with an axe.
Not to mention his confrontations with Van Pelt. He yanked the game out of this dangerous man's hands (knowing that this man has a gun), bites him on the leg when he grabs Sarah, and uses the aforementioned rocket launcher on him while his sister and Sarah pass the game to each other.
The stampede of animals, as they ran through the bookshelves and through the hallway. Again, as they run through the streets.
Alan bravely wrestling against a crocodile which was about to make a meal of Sarah when the house gets flooded.
When Van Pelt fires at Alan, Sarah attempts a Heroic Sacrifice by leaping in the way. She had no way of knowing there was going to be a Reset Button, and if there hadn't been, but Alan hadn't rolled the right number to reach Jumanji, her turn would have been next. Even if the game skipped her, she had no way of knowing if the others still playing would have ended everything and brought them back to life, but she still did it, anyway. Aside from showing she loved Alan, that's pretty awesome coming from someone who was so traumatized she had to spend two thousand hours in therapy for 26 years—and it's also her making up for having fled and left Alan in the jungle all that time.
A moment that is as much "Whoa!" and a bit mind-blowing as well as awesome: when Van Pelt fires, Sarah leaps in the way, and the bullet is halted in mid-air... only to slowly be sucked back into the game. As it goes, Van Pelt's gun and then Van Pelt himself begin to follow it... and you realize that everything the game released is about to be sucked back into the game too. The payoff was about as good as the anticipation.
Just the entireReset Button scene is awesome, given how you've seen Alan and the others go through so much hell and to see all of the mess the game has made get sucked back into Jumanji where it belongs is amazing, especially seeing Van Pelt's own freak out as he's dragged back into the game makes it all the more satisfying.
That Carl, despite having no clue what's going on, continues doing his duty as a police officer. When Alan tells him what's going on, he asks, "So what are we gonna do?" implying that he's perfectly willing to help him, even despite all the things he's seen. And even later, after seeing his whole car get eaten by a plant, he still makes his way with Aunt Nora to the house because he knows that's where the cause of all the stuff that's happening is.