I don't like reading baby books to the baby. They're so boring. It's stuff like "red, blue, green, yellow...purple!".
So instead, I read her the "Just So Stories" by Rudyard Kipling. I got the idea, after they were mentioned in Matilda. I only knew "The Elephant's Child", growing up. They had a VHS of that story, done by Jack Nicholson. That was the best story of the entire book.
Other good stories were "How the Whale Got His Throat", "How the Camel Got His Hump", "The Beginning of the Armadillos", "The Cat That Walked By Himself" and "The Butterfly That Stamped".
I disliked "The Sing-Song of Old Man Kangaroo"; it wasn't much of a story. As for the others, I'm ambivalent about them. The two stories about Taffy were cute, but "How the Leopard Got His Spots" struck me as vaguely racist. He gets his spots from a black person touching him; the idea being that someone touched their fingerprints all over a leopard, and their fingerprints left several groups of five spots.