I first read Wilhelm Hauff's tales when I was 10 yrs old, and fell in love with them. His stories are ancient, strange, exciting, beautiful and inspired from folklore around the world, from Middle Eastern cultures to Scandinavian ones. You'd have just as much fun reading them as the kids would.
Here's a few (spoiler warning):
"The Caliph Turned Stork" - the powerful Caliph of Baghdad and his grand Vizier, misuse a magic dust and find themselves stuck as storks. While learning to see the world in a differnt way, they go through a lot of trouble to turn back into men. This story has a lot of humour, I remember laughing out loud while reading it.
"Longnose the Dwarf"(or "Little Long Nose") is the story of Jamie (or Johan), a little boy turned into an ugly dwarf by a mean, vindictive witch whom he treated spitefully, because he was a bit naughty and thought she was just a defenseless old lady. She keeps him as a cook for years, but eventually he escapes and becomes a famous cook for an emperor; he finds a talking goose (Mimi), who turns out to be a girl who fell victim to the same witch. They become friends and end up helping each other break the witch's spells.
"The Adventures of Little Mook" happens in the Middle East; it's about an orphan servant who one day found a magic pair of slippers and cane, and goes through a lot of trouble and adventures while learning not to abuse his fortune. Unfortunately, Mook's appearance (his head was too big for his tiny body) always made him the butt of people's cruel jokes, and his new fortune was the cause of their envy and malice; he is so hurt and disilusioned by everyone that, in the end, he turns to a life of seclusion, and one cannot but feel for him.
"Stone Cold Heart" - the story of Peter Munk, the pennyless charcoal vendor who lived in a village in the Black Forest and gave his heart to an evil giant in exchange for gold; he becomes a very rich man, but his heartless ways lead him to a sad, lonely life. With the help of a gnome, who turns out to be his guardian little spirit, he tricks the giant into giving his heart back.
The edition I read had some other stories that were not present in later editions. Maybe the American publishers found their content a bit too strange for children, although I don't see anything wrong with them.
One story talks about the damage caused by rumors and superstitions: in a nordic village, a girl tries to prove she was brave enough to defy the legend of the undead old man who comes out of his grave every night at the stroke of midight; she goes into the cemetery at night to prove it and runs into the grave digger who was climbing out of a hole he just dug, mistakes him for the ghost of the old man and dies from shock. Funny, I think this story helped me as a child to never be afraid of walking into dark rooms.
Then there is the story of beautiful Fatme, or Fatima, who is kidnapped by pirates at sea and ends up in a powerful sultan's harem; her brother and his friend go through a lot of trouble to rescue her and another girl, while pretending to be physicians, but the only way they could examine a harem woman was by checking her hand/pulse through a small window.
There are more stories, but I guess you've had enough. Not every story has a happy, cheerful end, and some are a bit bloody and scary, but I believe that makes them more valuable; I think, as a child, there is no harm in learning to deal with danger, grief and loss in an imaginary world - prepares us better for future battles in the real one. In any case, should you consider buying this book for your children, I believe you'll be giving them more than just a book of old stories - it's a glimpse into the fantastic children's folklore of a past world we know little about, maybe a sense of history and continuity, and a chance to open their minds to something different.