Madeline, by Ludwig Bemelmans, 1939.
Recently, I read Madeline's Rescue to my five-year-old son. The story was fine, and the artwork was great, but it did make me nostalgic for the original Madeline.
Madeline takes place in another place and another time: Paris in the early twentieth century, when you were allowed a few weeks in the hospital to recover from an appendectomy. It may feel slightly foreign and dated to today's young readers, but, somehow, that just adds to its appeal. And the artwork, of course, is great.