I was at the library the other day and noticed a shelf of the complete Nancy Drew series, by Carolyn Keene. I loved these books in elementary school and couldn't help picking up "#5: The Secret of Shadow Ranch" for a quick read.
Other immensely satisfying series books from my childhood:
The Babysitter's Club - Ann M. Martin
The Saddle Club - Bonnie Bryant
Amelia Bedelia - Peggy Parish and Herman Parish
The Boxcar Children - Gertrude Chandler Warner
Ramona Quimby - Beverly Cleary
Goosebumps & Fear Street - R. L. Stine
What's on your list?