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Nightmare Fuel: Jumanji
The point of the game.
Alan's monologue after Peter tries reverse psychology to get him to play: "There are things that hunt you, in the night. Then something screams. And you hear them eating. And you hope to God that you're not dessert. Afraid? You don't even know what afraid is."
The ominous thumping noise of drums that comes from the game when it's buried.
Their effect on people. We see one of their victims, the realtor who sold Alan's house. She seems catatonic and according to a paramedic, she is suffering symptoms that resemble a heart attack.
That giant yellow plant that tried to eat Peter.
The lion's entrance. Peter senses someone...or someTHING... in the room with the two. Then, the lion's massive paws menacingly step on the keys of a piano...
Van. Pelt. Imagine it: a very good marksman who is interested in hunting you in particular. Let your guard down for even one moment, and you die. Alan has lived through that. He should be the one in therapy.
Van Pelt didn't just make Alan feel like a child. He was possibly hunting Alan SINCE Alan was a child. And who knows if Van Pelt ages? He could maintain that level of skill in hunting over the years, against an aging prey.
Also the fact that said hunter is indestructible. He did have a shelf of large paint tins fall on him and lived after all.
If you have arachnophobia, spiders the size of medium sized dogs will send you over the edge. The fact that they're rather pathetic puppets helps surprisingly little.
All of the discord and turmoil that the whole city goes through, just because of one roll of the dice sealing up Alan! By all accounts, that one factory was the major source of income in the whole town, and once his father went off the deep end and let it go under, the town's economy collapsed.
Nearly all of the animals unleashed by the game are darker scarier versions of real life creatures. Mosquitos are enormous and their bite kills very quickly. Monkeys are deliberately malicious and dangerous, throwing knives at people. Lions are larger and fiercer than in reality. Even the plants try to shoot venomous barbs at you on purpose. Only the herbivores like the elephants and rhinos are merely accidentally destructive rather than deliberately malevolent.
Even that is debatable; in the animal stampede through the city, some of the elephants take their sweet time in crushing the car that Peter takes shelter in.
The Cartoon Series
In the episode No Dice: Alan steals the dice, so the kids can no longer return to Jumanji and get in danger. He discovers that they repel the Game's threats... all but one: the Stalker. A Grim Reaper-like figure, implied to be at least the avatar for whatever sentience controls Jumanji, who wants those dice and is a total Implacable Man. He continues to follow Alan, wanting to kill him and restore the game, chasing him deep into the clockwork that make up the game.
The Stalker appears in several other episodes as well. He doesn't get any less scary. Not at all.
The scariest part about the Stalker is that when he recruits other villains, they are flat-out horrified by his appearence, including Van Pelt, who is described below.
Van Pelt is explicitly an Axe Crazy psycho in this depiction, who lives to kill anything he can find. In one episode, the kids have to sneak around in his house and accidentally wake him up while he's sleeping. They initially send him back by claiming to be the maid, but then he bolts upright and reminds himself that he shot the maid last Wednesday.
In episode 4, right before aunt Nora escapes from Van Pelt you can see heads of children on his wall.
The reveal that the game requires that there must always be a Hunter, so if you kill Van Pelt, you immediately take his place. Which means that Van Pelt might not be the first, but may just be an unlucky previous player.
Worse in that the above nearly happens to Peter, before Alan and Judy figure a way to bring Van Pelt back.
While the Fridge and Headscratchers pages argue that in the movie, Jumanji actually bends the rules to avoid killing its players, that is explicitly not the case here. The very first episode has Alan explain that most of his toys are the only things left of other kids who found the game and rolled the dice.