No discussion of Japanese adaptations of western works could possibly be considered complete without mentioning Nippon Animation. They nearly singlehandedly made anime based on classic literature into a genre of its own.
Their longest-running meteseries is World Masterpiece Theater, which Hayao Miyazaki worked on some series from. Among the many classics adapted to anime series were Heidi, Anne of Green Gables, Tom Sawyer, and The Swiss Family Robinson.
Heidi, Girl of the Alps was actually famous enough to be referenced in the Japanese version of Earthbound about 20 years later, replaced with the Beatles song “Yesterday” in the English localization. (Because “Hai” means “Yes” and it was basically “fill in the blank with a standard yes/no prompt”.)
(So, anime endings having weird visuals goes back at least as far as 1974.)
Though, in America, Nippon Animation’s best-known work is probably Grimm’s Fairy Tale Classics, which aired on Nickelodeon and was many American children’s first exposure to non-Disneyfied versions of these stories…not to mention they mixed some obscure ones in there anyway.
And they made more than a few other anime based on western works, including Alice in Wonderland, Maya the Bee, and an animal version of The Three Musketeers. Oh, and Future Boy Conan, Hayao Miyazaki’s directorial debut, was based on a novel by Alexander Key called The Incredible Tide, though in that case (and actually, probably Maya the Bee‘s as well) I think the Japanese adaptation is more known than the original work.