My first "too scary" movie was the 1999 cinematic masterpiece The Mummy starring Brendan Fraser. For those unfamiliar: not very scary at all, but I was probably eight when I saw it.
My siblings and I would fight over who got to sleep with the cat - in the movie the mummy is scared away by cats. Anybody who owns a cat knows this is a pointless argument, and the cat sleeps with who it wants.
The scary movie that got me was No Man's Land. A serial killer kills himself to avoid being taken to prison and his ghost traps the whole town while he goes on a killing spree.
I watched it again years later and it wasn't nearly as scary as I remembered. I was like 12 and it was 2 in the morning, so it chilled my sleep deprived self to the bone.
Oddly enough, this movie wasn't what gavee the worst nightmare I ever had. That honor belongs to the kids show Chalk Zone. The episode with the pink, hair eating frogs scared me in my dreams so bad I still get goosebumps just remembering it.