This is one of my favorite horror films, and I daresay one of my favorite films in general as well. Anyone who doubts that a horror film can be great art as well ought to give this one a try.
I will have to revisit this comment after viewing the film again, as it has been a while, but there were a few comments I thought people might find useful regarding the stories the film adapted.
Two of the stories can be found in Lafcadio Hearn's book Kwaidan: Stories and Studies of Strange Things. These are "Hoichi the Earless" ("The Story of Mimi-nashi-Hôïchi") and "The Woman in the Snow" ("Yuki-Onna"). The other two can be found in other books of Hearn's; I'm grateful to Kenji Inadomi for pointing out that "Black Hair" can be found as "The Reconciliation" in Shadowings, and "In a Cup of Tea" is to be found in Kotto: Being Japanese Curios, with Sundry Cobwebs.
Many of Hearn's stories can be found online, including all of the above except "In a Cup of Tea." Attractive early hardcovers of Hearn's books are pretty plentiful, though, and not terribly expensive either.
As some others have noticed, there's an uncredited adaptation of "The Woman in the Snow" as the "Lover's Vow" segment of Tales from the Darkside: The Movie (1990). It's not bad, but Kaidan (1964) is the one that got it right.
