Some of the Sanity effects in Eternal Darkness were genuinely creepy at the time. I remember one time playing late at night w/ the lights off, and I got the one with the bugs on the TV screen that really freaked me out at first until I realized it was the game haha.

Nintendo announcing 1,2-Switch..

Oh in a game? Yeah I’ll second Beneath the Well in Ocarina of Time. That game should not have been rated E, someone probably just played the intro and thought “Just some fairy-kid running through the woods smashing pots and cutting grass; E”. Also, personally I was never that scared, but my cousin was terrified of the Skulltula House.

Besides OoT I’d say Metroid Fusion, being constantly haunted by the SA-X while not being able to do anything other than hide somewhere is quite tense.

It was technically second party (Silicon Knights), but that bathtub scene in Eternal Darkness.. Nintendo published it, so close enough I guess.

That weird part in Earthbound where you go inside your evil thoughts or whatever.

Maybe that creepy sun chasing you in Mario 3, especially in world 8. It's actually a pretty frightening concept if you think about it.

Tingle. Just Tingle in general.

The announcement of their fee for online.

These two

Honestly, ten year old me was quite terrified and depressed when I left the temple of time as Adult Link to find Hyrule Castle Town in shambles and taken over by Redeads (their scream had already scarred me, so you can only imagine what I was feeling).

It was a scary and sad moment for me that stands out above all else. However I also felt a burning desire to find Ganondorf and put an end to his reign of terror. Call it Justice, fate, or even vengeance...whatever Nintendo was trying to do with thay moment...it worked.

I was 9 when I first played OoT. The intro scene always freaked me out, Ganon riding his horse with Zelda on board, stopping to glance at Link. God that freaked me at the time.

I would put the moment in Twilight Princess as well. I guess many of you know this: https://www.youtube.com/watch?v=HmrMAEFSCIs

Nintendo's 2008 E3 performance : 

The first time a blood moon happened in breath of the wild freaked me out a bit. I had no idea what was going on.
The ghost girl in Pokemon x/y was a very unnerving moment.
Pikmin series as a whole is terrifying at times.
In the first metroid prime when you go to the bottom of a room and the lights shut off and you get attacked by metroids bursting through there glass prisons.

Almost every boss in Donkey Kong Country 3 is scary. The music helps too.