
A well written, fast paced YA fantasy with a good sense of humour. Cimorene, an independent minded princess, runs away from home and volunteers to be the a dragon's princess, getting caught up in dragon politics, magic, and the machinations of rival wizards. This is the first book in a series of four.
But I liked the Dealing with Dragons series from Patricia C. Wrede (humorous), The Hero and the Crown and The Blue Sword from Robin McKinley, and the Dragon's Blood series from Jane Yolen.
As a male I enjoyed it, and one of my best female friends also remembers it fondly.
I'd also throw in Sabriel, as a YA fantasy novel that I really liked, that had a female protagonist who kicked ass (rather than was there to support a male, or something else equally stereotypical)
Wrede's Dealing With Dragons series is incredible, the Circle of Magic series is a good read (https://en.wikipedia.org/wiki/Circle_of_Magic), same with the Alanna series (https://en.wikipedia.org/wiki/The_Song_of_the_Lioness).