I'm perfectly fine with Bombadil out of the film versions of The Lord of the Rings. Then again, whilst Jackson's versions are cinema classics, I'd always argue one should read the novel first, as there is a lot that gets missed that would only work in a book (not just Old Forest/Bombadil and Goldberry/Barrow Wights).

As for Arabian Nights, I'm a big fan of Michael Powell's 1940 The Thief of Bagdad. I don't think that's particularly faithful either, but it's a damned entertaining watch with (for the time) incredible special effects. :)