I always liked Aesop's fables, many more stories which were older versions than I remember. I had a book of these as a kid. Grimm's tales were interesting and longer, including two versions in some cases. My sister had a book of these stories, which I read, too. Anderson's imagination is different yet, and even though my mother read these to us as kids, I can't say I remember any.
Aside, I had a book of Mother Goose rhymes, too, the biggest and longest book I owned at the time. Later, in high school, I had a book called "Mots D'Heures: Gousses, Rames", which was a kind of spoof of the original, but with nonsensical French words that sounded like the rhymes as spoken with a heavy French accent. I'm just sayin'.