The marvelous Skye of The Princess Portal recently wrote up her list of "books that I find very touching and inspirational, that carry me to another world and evoke some of the essence of fairy tales and what it means to be a Princess. Not all of these stories contain Princess characters, but they all express some of the beauty and magic that forms my world view and in some way have influenced me over the years." Sounds lovely, no?
Go take a look over at 50 Books: A Princess Reading List. Other readers have added their favorites in the comments. Here are some of mine:
Cornelia and the Audacious Escapades of the Somerset Sisters by Lesley M. M. Blume
Mandy by Julie Andrews Edwards
No Flying in the House by Betty Brock
The Girl With the Green Ear by Margaret Mahy (out of print, but not hard to find. All of her short story collections are wonderful.)