To be honest, I was never particularly crazy about any of the "book-set" openings. I know that, in ways, it helps to give the films a "classic" feel, but I always felt it distracts from the actual story/characters. If I had to pick one that succeeds the most, it would most likely be
Snow White's. I just like how they use text-only to set-up the film, and it reappears later after "I'm Wishing/One Song" and again after the Queen's death. In
SB,
Pinocchio and
Cinderella, they are show in the introduction, but are then forgotten about until the end (I realize that, in
SB, the book reappears after Maleficent's curse, but after the movie transitions to the cottage in the glen, it's never seen again). Still, I've always loved the color as
Cinderella opens onto the Tremaine chateau in the present, with the rain, and the purples and blues. Betty Lou Gerson does an amazing job narrating (who would've expected it?) and I've never felt "Cinderella" was a weak song.
The Sword in the Stone ~ I've always enjoyed the opening to this film. Although, in a way, the intro is a little out-of-sync with the rest of the movie. It's so serious (and well-done at that), that it would lend itself better to a dramatic adaptation of the entire Arthur tale, where SitS goes on to be mostly about the early years of education and mostly in comedic terms. But I still love the intro. (and the movie).
Hunchback ~ I agree that it's a very strong opening, but I'm not sure if I would agree that it's the "best." It's definitely
one of the best, though. The music is extremely powerful, and the lighting effects are amazing. This is the scene I remember most from seeing the film in theater--I remember the snow, the lightning, and the statues that stare down on Frollo being very...compelling? (trying to think of different ways to say "powerful"

). I also loved the ending line, "Who is the monster and who is the man?"
The Little Mermaid ~ Of course I was going to mention this one. To be honest, I've always felt the opening with Eric and sailors was one of the more boring parts of the film (I actually think I would prefer the extended version of "Fathoms Below" found on the Platinum, but I wonder if it would introduce Ursula too early? Still, the length shows "Fathoms Below" to be a better song than the short version does, and I appreciate it's extension in the musical), but it
really picks up on the underwater side of it. I love the scenery and the mood that it gives, with the whales, the sea anemones, jelly fish, etc. And then the first appearance of a mermaid (a part that I enjoy, but annoys me at the same time; because the animation/effects make them look almost too flat, and their arms move awkwardly in the first shots), and then the urgency towards the golden palace. It's all very powerful. And I love the variation of "Part of That World" they have alongside it--it's just a very classic melody.
Tired of writing.

I'll just say that I think some of the best openings are probably
Bambi,
The Lion King and
Beauty and the Beast. Not much to say without reiterating what others have already said.
And, yes, the openings to
Dalmatians and
Robin Hood are very clever.