It's always seemed kind of unfortunate to me that most people, if they have read any of his books, have only read the first Oz book, the one on which the movie is based, as I think it is one of the weakest. Compared to the amazing flights of imagination in (my favorite) Ozma of Oz, or in The Patchwork Girl of Oz for example, it seems a little bereft of whimsey. I've mentioned Ozma of Oz elsewhere in writing about modern steampunk, as Mr. Baum presents one of the very fist literary robots.
I don't know if there is another author who has ever been as attuned to what children want as Baum was. Something about his stories goes right to the center of childhood itself. I think it has so much to do with friendship and animals and the fact that nearly everything talks. If there's one dream shared by many, many children it's that one's toys and pets would talk back. In Baum's invented universe, they most often do. One of my favorite bits of retconning is in (I think) The Lost Princess of Oz, when all the animals ask Toto why he didn't begin talking like all the other animals from our world do upon entering the Fairy Land of Oz, and he says he just didn't feel like it.
Baum reportedly wanted to cease writing Oz books, as he had other stories to tell, so he kept on introducing elements such as the spell Glinda cast that would make Oz appear to outsiders as just a continuation of the Great Sandy Waste that surrounds it. All of this is documented in his author's notes at the beginning of each volume. Inevitably, he will end a book with Oz being cut off from us (and thus, Baum, The Royal Historian of Oz, will be unable to write any more installments). He also, inevitably, reports receiving a letter from a little girl in which she asks "What about wireless?", and his writing about Oz continues, as it did until his death in 1919.
His influence upon my life is incalculable. We had a full set of the Oz books when I was growing up and I read them all repeatedly. W.W. Denslow, who illustrated the first book, is considered one of the great illustrators of the Golden Age. But, John R. Neill, who illustrated the other thirteen books has always been more to my taste. I grew up trying to draw as much like him as I could, and his massive influence is still visible all over my work. I was a strange and lonely child, likely with an undiagnosed case of OCD, prone to list making of all sorts (I swear, I spent at least half my childhood alphabetizing). At one point, I went through all of Baum's Oz books and made a list of all the characters. I (of course) alphabetized them and then drew each one. I also remember drawing each of Princess Langwidere's thirty heads.
I haven't reread them all in years and years. I think it may be time to do so again. I will, of course, share my findings here.