Couple of stories, back in the day Ludicolo gave a lot of trouble in pokemon because I just couldn't figure his typing (therefore I didn't know his weaknesses)

Chozo ghost and the space pirates of metroid prime scared me a lot, often making me not want to play the game but it's such a masterpiece that I was able to overcome those fears.

I thought the princess in the first castle was going to be there. I was very sad when I found out otherwise lol.

I remember stumbling across the dark guild dancers in Daggerfall and quickly closing the door to my room.  I was shocked, scared, and very interested in joining.

I was naive to believe that i was getting Toy Story like graphics SMH

I was always scared shitless of Nemesis from Resi 3 that I would find the nearest safe room and come out thinking it's safe only for him to just show up again, It took me a while to realize that you had to just kill him and move on or try moving onto an important piece of the story but even then you'd have to confront him. Boy did I love the puzzles in the old Resi games though.

I thought turning my GBA on and off really fast until the light turn green again gave it more energy.

Damn I completely forgot about nemesis, but funny thing is I couldn't play the game as a kid I actually beat it when I was like 16 years old and even then nemesis still scared me a lot.

lol I was lucky my folks let me at the time (I was about 12-13), I think the whole killing Brad cutscene was what set up the fear initially, I mean seeing a guy have his face mauled by tentacles can do some crazy things to the mind of a kid, didn't help that the dread music would kick in just before he shows up and that would always cause me to run around like some headless chicken =P. When you get the mangum or rocket launcher though, that's a different story. 

one of my favorite things was when i rented the japanese N64 before it came out in the US. It blew my mind, later i rented star fox 64 and goemon before they came out in the US as well.
Besides that maybe getting my SNES with mario world. My parents wouldn't get me the SNES the first year came out and i was watching super mario bros super show every day and calling in the number to try to win a super NES when it came flashing on the screen. I did end up getting the SNES on it's second christmas, which was the longest year ever.

I used to think that if I flew for long enough in the training mode in Starfox SNES, I would reach the mountains in the background.