I just finished rereading the trifecta of "What Katy Did", "What Katy Did At School," and "What Katy Did Next," all by Susan Coolidge. Look I GREW UP ON HILARIOUSLY MORALISTIC OLD KIDS' BOOKS and find them desperately charming and I AM STILL TOTES IN LOVE WITH WHAT KATY DID. The sequels aren't quite as good but once you start you can't stop, you know?
( cut for spoilers for What Katy Did )I don't have a lot to say about the sequels. They're well enough (and I LOVE Rose Red, a school friend of Katy and her sister Clover; Rose Red is utterly delightful!) but they do not live up to What Katy Did. Of course, this might be entirely blamed on the fact that I didn't own the sequels as a kid, and was only introduced to them later, so they don't have the same nostalgia value. :P
(there are further sequels too, but they're not about Katy so I've never quite bothered to seek them out.)