1. The Henry Huggins/Beezus and Ramona series (Beverly Cleary)
These books were among the first I ever checked out at the library. I believe I began with Ribsy, the story of Henry's dog getting lost and finding his way back home. As a kid I dearly wished I lived in Henry's neighborhood, and some of my childhood adventures were in part an attempt to emulate him -- in the building of a clubhouse, for instance.
2. The Boxcar Children Series, Gertrude Chandler Warner
I saw these first at a book fair at school and grew inexplicably excited about them. The series follows the four Alden orphans and their dog, Watch. The orphans decided to run into the woods rather than live with their grandfather, whom they'd heard was "very cross". Eventually they learned that gramps was a swell guy and moved in with him, where they solved mystery after mystery. I had an entire shelf lined with their books.
3. Back in Action, Elvira Woodruff
Another bookfair prize: in this, a kid uses a powder to both bring his toys alive, and shrink himself down to their level where he has adventures with them. This appealed to me immensely because other than reading and wandering in the woods (like Calvin, only without a tiger companion) , most of my childhood was spent outside playing with toys, building forts and dungeons and such out of wood, cinder blocks, and other miscellaneous objects. (A wrapping paper tube was used as a slide to the Vehicle Pool, while big D batteries were explosives.)
4. Indian in the Cupboard Series, Lynne Reid Banks
Similar to Back in Actions: if you've never had the pleasure, this series concerned a magical cupboard which could bring toys alive. These toys were not merely sentient pieces of plastic: they were real people, and through them Omri explored the world of the past. Sad as it sounds, this series is probably responsible for my childhood knowledge of the French and Indian War and the Algonquin Indians.
5. Goosebumps, R.L. Stine
My mom bought me "Let's Get Invisible!" and it thrilled me. The books became an obsession of mine throughout childhood, to the point that my very conservatively religious parents were alarmed: while Let's Get Invisible seemed harmless, other covers sported mummies, ghosts, and vampires. Goosebumps was a national craze for a while: my home library even hosted a "Goosebumps Fan Club" .
6. Bruce Coville's sci-fi series
Strange as it seems, Aliens Ate My Homework! was probably my first introduction to science fiction. I hadn't encountered Star Trek before reading it, otherwise I would have been deeply amused at book three, The Search for Snout -- in which a human boy assists a multiracial crew of peaceful aliens in finding their logical comrade, Snout...who is missing and was presumed dead. He's something of a father-figure to the boy, who helped the aliens before in defeating a villain of some kind.
7. Redwall, Brian Jacques
It's um..like a medieval fantasy story, only with woodland creatures instead of people. Redwall was the first 'epic' novel I ever read.
8. The Matthew Martin Series
This is more preteen than childhood, but Matthew Martin was the ultimate cool kid for me. I didn't watch a lot of Saved by the Bell, but Matthew was sort of like Zach, only he could use computers. I can't remember much of what Matt did, beyond fighting with girls and later flirting with them.
9. Wayside School, Louis Sachar
Welcome to wacky Wayside Elementary! The city wanted a one-story school with thirty classrooms, but instead they got a thirty story school with one classroom per floor! One of the teachers is a witch, one of the students is possibly just an opossum wearing a lot of rain coats, the thirteen floor doesn't exist (except for when it does), and if you happen to get a bunch of cows on the top floor, they won't come back down. The book focuses on one classroom, filled with kooky characters. The series is absurdism for children, and I'd buy used copies for myself if I ever thought of it.
There was also a math-related spinoff series (Sideways Arithmetic is the book I remember) which adult reviewers call "quite clever", but which confused me utterly back in the day.
10. Great Illustrated Classic Series
Ah, the series which introduced me to so many books -- The Call of the Wild, Black Beauty, The War of the Worlds, Journey to the Center of the Earth, Robinson Caruso, Dr. Jekyll and Mister Hyde, Dracula, and Around the World in Eighty Days are just a few I remember. The books were abridged version of their real inspirations, possibly restyled in parts to be more readable to children growing up distracted by video games and television, and illustrated amply. For the past few years I've been revisiting some of the books I read in that series..