This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / EarthBound Beginnings
While not nearly as famous as the one in the sequel, the final battle against Giygas is actually pretty terrifying when placed into an appropriate context. If you were playing as a child in 1989, this was probably the very first video game battle you'd experience where everything you thought you knew about playing games doesn't help you. You can try and try with all your might, using all the amazing powers you'd earned during your adventure, but no matter how hard you try, he will just continue mocking your ineptitude, telling you your only options are to give up or die. Coupled with the white-on-black contrast of his sprite, the ear-bleeding eeriness of his "music", and the fact that there's a good chance you're in a dark room, for the NES, that was some pretty unnerving stuff.
A small one, but the quest to find Pippi is chock-full of Adult Fear. To start, Pippi runs off somewhere and disappears for a long time, which greatly distresses her mother. When Ninten finds her, she is hiding in a coffin in a cemetery that is occupied by zombies, and she's totally unprotected. There is an unused sprite titled "Gang Zombie" that resembles Pippi's clay model, implying that if Ninten hadn't found her in time, she would've been found and turned into a zombie. Then there's the fact that she has no father to speak of, which gives off some more horrible implications as to why she ran off in the first place...
The Rosemary's Mansion is an enormous haunted house that manages to be dark to the point of almost complete blackness in spite of the numerous torches hanging from the wall. Thanks to the borderline maze-like architecture, you'll probably end up spending a while there as you look for the haunted piano that teaches you the fourth melody, fighting off all kinds of undead mooks on the way and occasionally hearing laughter and even death threats from thin air. The spooky cave music doesn't help, either.