Classic for a reason.  There’s a constant sense of danger despite there not being many traditional horror scares.  Roman Polanski mines the terror from the people around Rosemary, probably one of the best illustrations of gaslighting in cinema.  The element of satanic cults and witchcraft often cause films to take a wrong turn by taking the audience completely out of what otherwise is a grounded character story, but Polanski manages it nicely here.  By framing the more outlandish satanic moments early on as a fever dream, he presents them in an easily digestible way before letting the psychological thriller story take over.  By the time we arrive at the chilling end, we buy into the idea that Rosemary has given birth to the spawn of Satan.  Polanski never belabors the mythology, nor does he feel the need to actually show the baby, allowing the viewer to fill in the holes, which can often lead to a more thrilling interpretation and experience.