I think the first one I remember is It with Tim Curry (technically a TV miniseries I think but whatever). I think I was maybe around 6 or 7 at the time.
I was roughly 6 or 7 when I saw Evil Dead 2 on VHS. Needless to say, it left a very lasting impression. Thankfully, it is mostly love and appreciation for the genre.
I think it was the Thriller music video, but I was pretty young and thought it was a full movie. It played before the main feature at a drive in movie.
After that I think it was The Fly. The arm wrestling scene still scares me.
My wife told me a story about how Tremors was her first horror movie. Her dad actually woke her up to watch it and said "you've got to see this!" because he thought the movie was so awesome. Scared the hell out of her.
Terminator 1 definitely counts as a horror movie. It's basically a slasher movie with the unrelenting machine coming to kill someone, but has a pretty cool backstory. Better than "oh he drowned in the lake".
My first was the network-televised version of Poltergeist. Being a kid, it was still plenty scary. My dad waited h til I was in bed, then came down the hall scratching the wall. I nearly shit myself.
I really don't remember. I know Creepshow must be one of the oldest ones and Tales from the Crypt. Jaws might be, too. And the 50's version of The Fly and Asphyx are old ones but I can't remember when I've seen those myself. Long enough ago to not remember. Let's say under 10 anyway, most likely.