I remember a lot of these books from before I could read, and from after. I don't think I started reading particularly early, but of course I was read to long before that. (I also don't remember childhood particularly well; possibly this is because I lived in Switzerland the year I turned 5, and then moved to a different city in the US the year after we got back; so I didn't see many of the same people or places to refresh early memories.)
Some of these books still mean quite a lot to me. Many adults may find this strange, but I suspect not those of you who've managed to make it this deep here!
I have no idea how these books would play to today's children, or how they would play to an adult who hadn't read it in childhood, because I'm neither. If people can't find pleasure in these books now, that's their loss.
The Wind in the Willows
Kenneth Grahame's classic was a big success with me. Rat and Mole and Badger were real people who I liked. Toad wasn't. He was something of a caricature, and not too much like anybody I knew. He was so stupid. He was annoying.
A few years ago I managed to find the very edition of this book that I remember, new (it's an umpteenth printing, of course). The illustrations are marvelous still, as is the story. Just now I found more than 100 references to it in Amazon's catalog; there appear to be more books, or perhaps it's been published in a multi-volume edition or something. It's a darned thick book as I remember.
And remember, there is nothing, but nothing, so worthwhile as messing about on the river in boats.
It was very British; I think I understood these partly as alien-culture stories.
Disney made a movie of this; the less said about that, the better.
by E.B. White.
He's a talking mouse. He drove a little car. He interacted in an intelligent, civilized, manner with people. It was fun.
E.B. White also wrote Charlotte's Web.
The Phantom Tollbooth
By Norton Juster.
This is a wonderful, intelligent, book. Milo receives a present, consisting of a toy car and a toy tollbooth, and a token. He drives past the tollbooth into a rather strange world, where he encounters the mathemagician, the 2/3 boy, and the island of conclusions (set rather far out in the sea of knowledge; you get there by jumping; to return to the mainland you must swim). This book is full of word play.
Illustrated by Jules Feiffer, too.
Somehow, I don't reread it a lot, which is strange for me and a book I like this much. I also don't remember anything important it taught me.
The Mysterious Island
By Jules Verne
Although the Nautilus and Captain Nemo appear at the end of the book, this is essentially a survival adventure story. It's full of people who know how to do things, and do. It contains the theme of making the tools to make the tools to make the tools, which appears again and again in SF.
Again, I got in adulthood the same edition of this book I was used to reading from the library. It has gorgeous illustrations by N.C. Wyeth. The Amazon link above points at this edition, in fact.
More memorable books from my childhood.