Extracted from Aroduc's 2011 Summer Anime preview:

A series that seems to inspire one of two things in people, an intense love [...], or the compelling urge to take a nap.

However fond I am of Natsume Yuujinchou, I have to more or less agree with Aroduc here. NY is pretty much a bunch of heartwarming slice of life stories that just happens to be about the supernatural (or mostly about the supernatural). Given my usual tastes, I have no idea why I like it so much, and I certainly can't recommend it except very selectively; it would bore or annoy a great many people.

(But if quiet, heartwarming stories about the supernatural sound like your kind of thing, you really owe it to yourself to check it out. Consider this a strong plug. You could probably start anywhere without losing much, but starting at the beginning of the first series isn't going to hurt.)