Personally I've been kinda creeped out by some stuff, mostly the undead enemies and areas in The Legend of Zelda: Ocarina of Time, the piano in Super Mario 64, etc.
But it's never gone as far as to actively give me nightmares or get me thinking about anything like that when not playing the game.
Well games designed to be scary are an obvious big ticket for this sort of discussion, and in the rising popularity of the internet during my childhood there were plenty of those. I remember being unnerved by the original Slenderman game and fearing he would appear in my room in the dark of night, though looking back I don't see what scared me so much. I think I was more scared of the superstition and theorizing around such topics by the fans... which reminds me...
This one might not fully count since it technically wasn't in the game, but it was official so I'll say it. The ending scene from the Luigi's Mansion E3 2001 trailer is probably what tugged at my fears the most as a kid, squarely because of what others thought of it. By itself the scene is rather confusing since it isn't in the game, and Luigi doesn't ever assume this morbid expression either. But years after the game's release, it was ripe for fans to theorize that this was something left-over from the beta, and for good reason. It gained the false identity of an unused game over screen, with different reasons all terrifying to me: from Luigi being possessed or a zombie, to him being depressed that he couldn't save his brother in time (which tied to a timer mechanic, also unused in the final game). Painting the scene as some sort of horrible bad ending really unnerved me! Though I of course now know that it was never part of some cut bad ending, and was just made for the trailer.
Oh there are so many things lol. There's the Luigi's Mansion Beta like @Really Ilini said but also slightly creepy thumbnails I'd come across for a split second (yes that would prevent to sleep for a day). There was also the Sonic CD Majin Sonic easter egg but worst thing by far was Omega Flowey.
When I was younger, I was getting interested in Undertale watching all sorts of videos about it, until one day I came across Omega Flowey and that actually gave me nightmares for a week and I became an Undertale hater despite having never played it just because it scared that much. I remember I used to have a plushie that looked like a flower attached to my lamp... well I used to hide this thing because it reminded of Omega Flowey. For the 2 next years or so getting reminded about Undertale made me very uncomfortable. By the way this story I'm telling has absolutely 0 exaggeration. I was actually that much of a coward. I'd like to lie and say I was about 7 years old but in truth I was more like 11 or 12.
Now I don't hate Undertale anymore, I got over it obviously and I did finally play Undertale a few months ago. It was pretty good, not amazing but definitely a good game.
