EDIT 2/2017 - I've added ADULT, YA, or MG to designate the original intended audience Adult, Young Adult/Teen, or Middle Grade.
Dragonriders of Pern - Anne McCaffery (Start with Dragonsong, or the short story collection A Gift of Dragons is excellent and even contains a story with a tween-aged protagonist!) Many people have concerns about this series because there are sexual consent issues. ADULT
The Girl Who Owned a City by O. T. Nelson (One of my favorite post-apocalyptic novels - written before that was even a genre!!) There is also a graphic novel version. YA
The My Teacher is an Alien series by Bruce Coville (I devoured these in 4th grade! I also recommend Jeremy Thatcher Dragon Hatcher and most of his other books!) MG
Handbook for Dragon Slayers by Merrie Haskell (Not your typical "princess" story, way better! - Themes in this book include being differently-abled, bravery, duty/desire, bullying/mistreatment, kindness, strength, and not judging a book by its cover.) MG
