I've read plenty of Andersen's stories, and I just can't bring myself to appreciate them. They're too cruel and violent, with many perfectly good characters suffering permanent disabilities. Like in the original (not the Disneyfied) Little Mermaid, where the mermaid not only lived the last days of her life with painful walking and inability to speak, but also died for no reason (the prince didn't love her). Or in Constant Tin Soldier, where all characters died, making the whole story pretty much a waste of time: one melted and the other burned up. Or Thumbelina, with a happy ending, but very creepy events along the way, like a dung beetle and a mole rat trying to marry the little girl (that is, force her into marriage).
I guess Brothers Grimm's fairy tales are also violent and bloody, but it's more detached, and you don't really feel the cruelty. The characters in their fairy tales still suffer violent deaths, but it's more like "well, that was the society at the time", and there's often some sort of reason for it. For a modern point of reference, compare a bloody shooting movie, like Die Hard or Skyfall (Grimm), with torture porn like Saw or Hostel (Andersen).