In Japan Pooh is popular: even grown women will own Pooh key rings, bags, underwear, and so on. And many of those items get proudly displayed in public! Disney made Pooh popular, but these book are the original stories, and one of the lovely things about being a parent is being given the chance to read them. They are popular with my children, so I have had plenty of chances.
As a side note the Disney movie is also good. It is gentle, funny and the kind of thing you can show to your children without having to worry. There is just one scary scene (where rabbit is lost) for a young child. The animated TV series, and the Tigger movie, are only loosely based on the books and suffer for it. They are watchable enough, just not as good enough as either the original Disney movie or the books.
In the books the personalities of the main characters are more distinct and better developed than in the movie. Eeyore in particular is wonderfully funny. A few times my children have been almost asleep, as I have read them these books, and I have woken them up again by giggling at Eeyore's manic depression. "Daddy, why are you crying?"
(Note: I have the paperback editions, but it seems only hardcover versions are being published at the moment.)
Winnie the Pooh: Complete Collection of Stories and Poems (both books, hardcover): UK JP
Winnie-The-Pooh (hardcover): UK JP
The House At Pooh Corner (hardcover): UK JP
The Many Adventures Of Winnie The Pooh (DVD): UK JP