The first horror movie that I had to walk out on because it was so scary was when I was 13, and it was Pet Cemetery. It's a fairly tame movie by today's standards, but the special effects of the things coming back to life just freaked me out.

Since I was more into scifi/fantasy because of my imagination, I didn't watch many Horror movies because of that over-active imagination. I was 11 when I saw my first two, and both of them kept me awake at night for a number of days afterwards.
One was called The Hand (made in 1981), and the other was called Piranha (made in 1978). Jaws was also an early one that I remember watching, so the two aquatic ones made it difficult to go into the water for a while as a kid.

Since then it's suspense horror that affects me more, as gruesome horror is more fascinating for thinking about how they did it with special effects. (unnecessary gruesome special effects in non-horror movies is not something I like, but contained within the horror genre, it has a purpose for the film-maker to flex their creative muscles, and therefore has a place on screen for "entertainment" purposes - whereas a non-horror movie that has excessive blood and gore is redundant when the genre or entertainment focus is supposed to be action, adventure or drama)

Suspense horror movies that I found scariest (as in, is still scary when watching it a second time), include Event Horizon (still creeps me out, but is a scifi movie as well so it fascinates me as well), The Ring (the American version), Poltergeist, Arachnophobia, It (I ended up watching it so many times that I don't find it scary anymore), Paranormal Activity, and Critters.

When doing a search online for what others think are the "best" or "scariest" horror movies, a lot of them are really old or gained critical support for being the first to be doing something... as such, I've seen most of them and don't find them very scary (I guess modern movies has desensitised me).
One movie that keeps showing on or near the top of various lists is the 1982 movie "The Thing", which I've never seen, but probably should since it seems to rate very well.

On the topic of horror movies that failed to be scary, I'd have to give a mention for the original Nightmare on Elm Street films and TV series, which became more amusing than scary over time... particularly the TV show.

As for a horror parody, I recommend watching the "Scary Movie" series, with my favourite being the second one. I've actually found that these horror spoofs make the original horror movie almost completely un-scary, as you keep thinking about the comedy element related to it from the spoof movie.