Princess Cimorene from Dealing with Dragons... by... Patricia C. Wrede. The series of books is called the "Enchanted Forest Chronicles."
I *worshipped* these books when I was younger. They were vividly created worlds in my mind, I could touch and feel them and I could jump into the mind of which ever character I felt like.
In case you don't know: Princess Cimorene ran away from home because it was boring and she wanted an adventurous life. But what is properly appropriate for a princess looking for adventure? Oh yeah--getting captured by a Dragon... except in Cimorene's case, she gives herself up to one Kazul who basically becomes her employer, her protector and provider. They build a friendship, and Cimorene does NOT want to be rescued from her dragon.
She's a great, practical, headstrong princess. Not afraid to get her hands dirty. (Which is why she's wearing her cleaning clothes and holding a mop handle.