Definitely Nancy Drew. Some good suggestions already, but I might also recommend:
Anne of Green Gables
Heidi
The Little Princess
The Secret Garden
The Wizard of Oz (but I'm sure you've already thought of that one!

)
A Wrinkle in Time
Any of the Trixie Belden series
Rebecca of Sunnybrook Farm
Any of the Marguerite Henry books (I loved the Misty books)
Alice in Wonderland
Peter Pan
That's all I can think of right now, but I'm sure more will come to me later.