The Anne Shirley series by L.M. Montgomery - She's an orphan. She's spunky and sassy. She's a dreamer and a daredevil. She's Anne of Green Gables. Read the eight books in order and see Anne grow up. From her days as a student in a one-room schoolhouse to going to college to becoming a teacher, her school smarts are just as important as her people smarts.
I'd add these....
Trixie Belden - So much cooler than Nancy Drew. She's a career-woman detective first and above all else. She has a temper, a strong will, an independent spirit, and a nose for mystery and trouble.
Meg Wallace - Especially in book 2 (A Wind in the Door), I think Meg comes into her own powers and finds her strength.
Turtle Wexler (The Westing Game) - Anyone who can inflict that many shin bruises in one book -- while solving a mystery and striking out on her own path in life -- is okay by me.
And of course, don't forget about this great Cool Girls list from Jen Robinson.
Who would you add?