I was quite fond of EB too - I liked Noddy, and there was a story called Treacle Pudding Town I used to take a perverse delight in. And her fairy stories.
For picture books I really liked The Story About Ping by Rosemary Sutcliff, and a Maurice Sendak one called Higglety PIgglety Pop, or There Must Be More To Life. Also one by Wlliam Steig called Caleb and Kate. And all of Beatrix Potter, but I especially loved Jemima Puddle Duck and the Two Bad Mice. Uncle Wiggley and the Sugar Cookie, mainly because it had a map in it and similarly the Fern Hollow books.
For older kids books I was very fond of the Madeline L'Engle books, both the Wrinkle in Time and Meet the Austins, I loved The Secret Garden, Black Beauty, My Side of the Mountain, The Dark Is Rising sequence, Mrs Frisby and the Rats of NIHM. I also spent a lot of time reading mythology at that age, mostly though not exclusively Greek and Norse. Though at the time all of them kind of ran together in my mind. The Mysterious Tadpole by Steven Kellog. Miss Nelson is Missing.
I work in a library and I will say that there aren't huge numbers of newer children's books that catch my eye, they tend to be very didactic with rather poor story telling. I do rather like the Gregor the Overlander books, which have a great narrative tale. Not really newer but an adult discovery for me is the book A Teeny Tiny Baby which is often found as a board book. I'm sure there must be some good modern picture books but none come right to the front of my mind as favourites.