Horror is a tricky thing. There's a very fine line between fear and silliness, and if you don't sufficiently creep someone out, they're just going to think you're funny -- or stupid. That's why American Horror Story is a breath of spooky fresh air.
You wouldn't think television would be the place for it. Most horror in the media has traditionally come from movies, which are easier to be taken seriously for a number of reasons. Perhaps most importantly, it's because monsters don't have to wait for a Febreze commercial before they can start attacking again.
Horror literature has a rich history, but it isn't as visceral or immediate as anything on the screen. It might stick with you for longer, but you have build up the right amount of fear for it to work.
American Horror Story succeeds primarily because it features characters viewers care about. They sympathize with the people on screen and feel for them. If you don't believe me, just watch this new promo for the upcoming season of the show (via Vulture). The return to the air is being timed with Halloween, so you should be in the perfect mood to be utterly freaked out by then.