Man, this thread takes me back. I was like 10 when I got Diablo, and there were parts of it that scared the crap out of me. The Castle levels especially were just creepy as Hell. Even as a kid, I recognized that every enemy was basically the same thing, a walking assemblage of hitpoints and attacks that walks up and tries to kill you. Not that scary really. But the Castle, the haunting music, the ambient sounds, and the pitch black hallways. It didn't help that the Castles were where the bogeymen first appeared, but they themselves were not that intimidating. I always felt like there was something truly monstrous, in a way the enemies were not, lurking right outside your little circle of illumination. Waiting, following, never attacking. Maybe even an army of them, calling from the shadows and the cracks you couldn't crawl through.
The Caves were also scary, in the more practical sense that any second you could be hit by a hailstorm of magma and acid globs. And the Hell levels kept making me think that something really crazy was going to happen, but instead you just chase Harpies around for hours. I kinda spoiled Hell by reading part of a strategy guide though.
And as for the Butcher, like the second time I fought him, I was playing a Rogue, for the express purpose of locking myself in a "jailcell" room and shooting him through the bars. He got in with me. I shot him to death without missing once, the fat bastard stuck in a loop of hit-animations until he went down. Never held much concern after that.