The first movie monster I can remember seeing as a kid was the Gill Man in "Creature From the Black Lagoon" (1954). I was about seven, and I never saw the movie back then, but I know I saw the preview a couple of times. I couldn't tell whether the movie was any good (I'm not sure I cared), but I knew I'd never seen anything like the Gill Man before. The image took up residence in my young brain and has never quite moved out.
Another monster I remember from back then (and another movie I didn't see) was "Rodan" (1957). Rodan was a giant flying reptile, one of many nuclear-age Japanese monsters that followed in the wake of Godzilla, and for a short time, the trailer for the movie was all over television. My folks saw the trailer, too, and said, "Don't waste your money," which was sound but irrelevant advice for a kid who (they knew) didn't have much money.
Another note about "Rodan". I finally saw it more than 50 years later on cable TV, and at first I thought I was watching a remake. Then it occurred to me: The televisions we were watching that trailer on back in 1957 were all black-and-white, and I always assumed the movie was, too. I had no idea "Rodan" was in color.
My favorite monster movies as a kid were the classics from Universal, the Dracula/Frankenstein/Wolf Man/Mummy movies from the '30s and '40s. I watched them all on television, starting when I was 10 or 11, and I loved their shadowy atmosphere, gothic sets and the actors who played the monsters, especially Lon Chaney Jr. and Boris Karloff. I don't remember ever being frightened by them. What struck me was that the monsters - almost all of them - were tragic. They didn't want to be monsters. They were cursed.
"Rosemary's Baby" (1968) creeped me out, partly because its satanists were so ordinary - your friendly, aging neighbors in the coven down the hall - and (especially) because Roman Polanski (spoiler alert!) never shows you the baby.
But the scariest monster movie I ever saw, that's easy: "Alien" (1979). I was an adult by then, in my 30s, and I knew the setup, and I knew it was just a movie, and it still scared the crap out of me. Part of that had to do (again) with the ordinariness of the characters, but mostly it was H.R. Giger's set and monster designs and the direction of Ridley Scott.
The ship - a rust-bucket freighter - was such a dimly-lit mass of pipes and tubes and odd pieces of junk, that you never knew for sure that the monster wasn't part of the ship. And once the alien chewed its way out of (spoiler alert!) John Hurt's stomach, you knew that all bets were off, the monster could be anywhere, and nobody on the ship was safe.
A monster that's infinitely resilient, apparently unkillable, scary as hell and ugly as sin? What's not to like about that?
And did anybody else watch Sigourney Weaver taking Jonesy with her at the end and think, oh, no, don't do that, the alien could be in the cat?
I sure did.
