This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / The Legend of Zelda: A Link to the Past
Ahh! Kill It with Fire! note Literally. The only way to go inside is to burn the mouth with the Fire Rod.
The manual describes how Ganon got his hands on the Triforce, corrupted the Golden Land, and became a beast.
After vanquishing his own followers, the leader stood triumphant before the Triforce and grasped it with his blood-stained hands. He heard a whispered voice: "If thou hast a strong desire or dream, wish for it..." And in reply, the roaring laughter of the brigand leader echoed across time and space and even reached the far-off land of Hyrule.
The basic soldiers have very good AI and will actively chase you if they see or hear you. They can also disguise themselves as shrubs and only appear when you cut one, or hide in grass to snipe you with crossbow bolts.
Agahnim stations guards right outside Link's house, meaning he knows where Link lives.
Link is framed for Zelda's kidnapping at the start of the game, making Kakariko Village an unsafe place to be. If citizens see you, they'll sic guards on you until you leave the screen or kill the guards.
The music in the Dark World before you obtain the Moon Pearl. Try accessing the map screen and you see a lifeless, gloomy, twisted version of Hyrule laid out while that music is playing. The lack of warning before this segment, combined with how sudden the atmosphere of the game changes is downright unsettling at best, but seeing as many people started playing this game as kids, it wouldn't be surprising if they lost any sleep from this segment solely.
This is the first dungeon where the Wallmasters make their ceiling-falling debut. (Though they were in Zelda I, they came out of walls in that game.) Even though they aren't as terrifying as the 3D ones, just think of being a kid playing this game for the first time and randomly getting grabbed, pulled up to the ceiling, and returned to the entrance by a disembodied hand.
THE GORIYAS. In this game, they're fairly large, they mirror your moves (the red ones also shoot fireballs), and there are black hollows where their eyes should be. Did anyone miss the boomerang-throwing they used to do?
Here's some Fridge Horror: The most common enemies you fight in the Light World are brainwashed human soldiers, members of Hyrule's military. You're killing members of your own side whose minds have been enslaved by their enemy. And imagine what things will be like after Agahnim and Ganon have been defeated for the families of the brainwashed soldiers.
It gets worse when you talk to one of the soldiers around the castle, before you get to the ones that attack you, who says that everybody around him seems to be turning evil, and surrenders to the likelihood that whatever is doing that will get him soon.
It's implied that the World-Healing Wave at the end undoes this, as the King and Link's Uncle are shown alive and well at the end - so why not the random innocent mooks you killed?
Agahnim is probably one of the most competent Zelda villains; he kills the King and apparently vaporizes the maidens, including Zelda—the latter right before Link's eyes. When he's defeated the first time, he transports Link to the Dark World. The only reason that Link survives is because Agahnim had no way of knowing that Link has the Magic Mirror, or possibly no way of knowing that it can warp Link back to the Light World.
In the opening to the game, you can see the Hyrule King deader than dead (meaning only his clothes and bones are left).
in the GBA release you're forced to watch the intro every time you start a new file, whereas in the original SNES version it only came up as long as you didn't press start on the title screen.
The many thieves lurking in both the Lost Woods of the Light World and the Village of Outcasts of the Dark World. They follow you constantly (unless you fake them out and leave them obstructed by a tree stump of whatever), if you do encounter them directly, they bump into you without warning and make off with your hard-earned goodies(!) like Rupees and bombs before you can even grab them back for yourself, and both versions by themselves are pretty creepy in their own right. Since animals replace people in the latter, when you first see it, you think nothing of a random fox until it approaches you and the former has a permanent scowl on his face and has white triangles where his eyes should be. The worst part is that they're the only enemies in the game that you CANNOT kill. No matter how many times you slash them, shoot them, bomb them, or even blast them with magic.
If you exploit some glitches to battle and defeat Agahnim early in the game before you get the Magic Mirror or Moon Pearl (as mentioned under Unwinnable by Insanity), you get transported into the Dark World, where you get transformed into Bunny Link and can do absolutely nothing beyond wandering around helplessly until you eventually get killed. In addition to being a scary enough concept in itself — not helped by the somber "Bunny Link" theme playing as he gets pelted by spears and bombs from the assorted enemies — the horror of the situation is turned Up to 11 when you realize this was the fate of everyone who wandered into a magical transporter or got zapped into the Dark World by Agahnim.
A bit Fridge Horror: Agahnim turns Hyrule Castle's gate into one of these transporters, meaning anyone so much as visiting it got subjected to the same horrible fate.
This is the first game in the series where Ganon has the entire Triforce, rather than just the Triforce of Power.
A telepathy tile in the Swamp Palace explains that objects exist simultaneously in both worlds, and that the state of the object in one world affects the other. With that in mind, think of the trees. In the Light World, certain trees have goodies that fall out when rammed into. In the Dark World, the trees standing in the same place as those trees are people you can talk to. Puts "Quit bothering me, and watch where you're going when you dash around" in another light, doesn't it?
Blind's Hideout. At one point in the dungeon, you find one of seven lost maidens you are to rescue. So after leading her into a big, empty room with a big patch of sunlight, she screams "GYAAGH! TOO BRIGHT!" and Surprise! It's actually Blind, the boss of the dungeon! The young, pretty "maiden" is now a big, ugly red monster that floats around the room, shoots fireballs everywhere and sends out his multiple heads to do the same thing.
Some of the artwork follows this interpretation, going so far as to show Link, back turned, express dawning horror as the fake Maiden has transformed into Blind, almost like something out of a horror movie or creepypasta....
Reading certain headstones in the Sanctuary's cemetery will cause a ghost to pop out of the top of the grave and give you chase, albeit slowly and through levitation. Even better, the exact same happens in The Legend of Zelda: Ocarina of Time if you go into their cemetery!
Ganon might look like a silly blue fat pig man here, but remember: according to Hyrule Historia, this is the same Ganon that killed the Hero of Time and took the Triforce of Courage from his dead body.
This game's representations of the Zoras. While in Ocarina of Time they're a race a beautiful humanoid fish people who help you, here you have these creepy swamp creatures that resemble a catfish's uglier brother. Worse, although half of the creatures shoot fireballs at you, the other half will jump out of their puddles and follow you! And let's not mention the leader of the Zoras (although he's Good All Along, selling you the much-needed Zora flippers). Ironically, the Dark World's versions of them, which usually have a twisted version of their Light World equivalent, are more friendlier-looking (but no less dangerous.)