This is probably the darkest (literally) Disney cartoon made, even eclipsing Snow White for dismal castle scenes and skeletons. My daughter, then 7, simply didn't go for it and found it 'far too scary' towards the end - the Barbie and Cinderella films are more her bag. My son at the same age loved it however, and I quite enjoyed watching it with him as well. The story involves a young boy farmer (who has dreams of being a great warrior) and his magic pig, who both search for the mystical Black Cauldron. The scene with the three witches who guard the Black Cauldron is a highlight in a pretty consistent film (once the story gets going). OK, some of the characters, well one really, the Bard, are a bit wet, and occasionally the slapstick seems out of place, but the cosmic struggle between good (the farm-boy Taran) and evil (the Horned King) is well done and there a few nice touches. Personally I prefer the older 'Sword in the stone' though which has a similar feel, as it's also a medieval fantasy, although that one's relatively pig free. However do have a look at the excellent book this film was adapted from: The Black Cauldron (Chronicles of Prydain) by Lloyd Alexander, aimed squarely at preteen boys around 10 - it's part of a cult series of books first published in the 1960s.
This film is strangely reminiscent of the earlier 1982 film - Conan the Barbarian, particularly the tomb sequence where Taran finds the enchanted sword. Although this film is a little scary for most little ones despite the U rating, the humour lightens the film considerably and it's no more frightening than Sheer Khan's sequences in The Jungle Book really. Overall I think older preteen children aged around 7+ (and more likely a boy I suspect) would enjoy watching 'The Black Cauldron' few times.