The Nancy Drew mysteries.- They're great. And last night I just came across the Dorothy Dale books by Margaret Penrose that I really want to try out. I was rereading the Little House on the Prairie books by the time I was 8 and starting Anne of Green Gables. Laura and Anne have always been my idols- I'm almost 30 and I still occasionally think, "What would Anne do?" :) They influenced me to become a teacher.
The BFG by Roald Dahl. Not a series, but Sophie is brave and loving and thinks outside the box. Definately a must read for ALL kids.
Also you might try the Oz books by Frank L. Baum. More imagination than real life, but Dorothy shows ingenuity, courage, and empathy.
Not series books: the Great Illustrated Classics version of any Jane Austen book (Pride and Prejudice and Emma are great) or Little women by Louisa May Alcott.
These are all books that I loved at that age and stayed a part of me. Does this help?