Esoteric Happy Ending: In The Cripple, a paralyzed boy manages to drag himself out of bed and attempts to walk so that he can save a caged songbird from a cat creeping up on it. Everyone celebrates the child's improved state, but in true Andersen fashion "the bird, of course, had died of fright."
High Octane Nightmare Fuel: There's a story about a fir tree that dreams of being a Christmas Tree because of the honour and the glory. Getting cut down hurts like getting your legs cut off. Then it slowly dies, like Christmas Trees do.
The hellish punishment in The Girl Who Trod on the Loaf. The Red Shoes, where the heroine is only saved from damnation by having her feet chopped off. And the literal nightmare in Aunt Toothache, featuring the Anthropomorphic Personification of aforementioned ailment, who has drills and tongs and similar implements for fingers. It is possible to go on...