Secular Books:
Amelia Bedelia by Peggy Parish
Picture books for young kids.
Nothing objectionable.
Recommended
Charlie and the Chocolate Factory
and its sequel
Charlie and the Great Glass Elevator by Roald Dahl
The adventures of Charlie in the chocolate factory and then in a glass elevator / spaceship owned by an eccentric and magical man.
Chapter books.
Cautionary notes: some parts may be scary for young children.
Recommended
Pippi Longstocking Series
and
Bill Bergson Series by Astrid Lindgren
Pippi Longstocking is a well-known series about the adventures of an independent little girl who lives on her own, her two friends, and her father who occasionally drops in on her.
The Bill Bergson series is actually much better, but never made it as big in the U.S. and may be difficult to get, since it has been out of print in a while.
Bill Bergson is a boy who with his two friends has many adventures.
Cautionary notes: some parts may be slightly scary for very young children. Some very yeshivish parents may not like these books.
Both recommended.
Beverly Cleary books.
Chapter books.
You can get used copies of 15 to 20 of her books at a time on Ebay relatively cheaply.
Recommended
Time at the Top
and its sequel
All In Good Time by Edward Ormondroyd
Time Travel / Adventure.
Chapter books
A young widow and her two children travel back in time via a magic elevator.
Fascinating stories with satisfying conclusions.
Cautionary notes: none
Highly recommended
Encyclopedia Brown series by Donald J. Sobol
Collections of short stories, where the boy detective hero has to use clues to figure out whodunit and/or prove the guilty party.
Some stories have not aged well, but overall fun for kids to read and try to figure out.
Cautionary notes: none
Recommended
Lewis Sachar books.
All of his books are well-written.
Chapter books for 8-14 year-olds.
Cautionary notes: Parents may want to read the books first, just to make sure they are suitable for their kids.
Recommended
Matt Christopher books.
Somewhat dated, but still good for sports-loving kids.
Cautionary notes: none.
Recommended for sports fans.
The White Mountains series by John Christopher
Chapter books.
Science-fiction / adventure.
Post-apocalyptic world controlled by aliens who patrol the earth in huge machines.
Highly recommended
Babar Series by Jean de Brunhoff and his family
Picture books.
The adventures of the elephant king.
Cautionary notes: very small kids may be scared by the evil rhinos, and the accidental death of the old king.
Highly recommended
Chapter books.
British adventure / detection series involving a group of five kids.
Recommended for kids who like this genre.
Richard Scarry books.
Oversize picture books with well drawn and memorable characters and stories.
Cautionary notes: none
Highly Recommended for small kids
The Wizard of Oz series by L. Frank Baum
Chapter books.
Adventure / magic.
This series is best read in order.
Can be read aloud to children of all ages.
Cautionary notes: none
Highly Recommended
James and the Giant Peach
Chapter book.
Adventure / magic / offbeat.
The adventures of James on his journey with oversized bugs in a massive peach.
Recommended
Jewish Books:
The Adventures of K’tonton
Recommended.
Dov Dov stories by Yona Weinberg.
Entertaining series of story books, usually with lessons / morals, for younger kids.
Recommended
Gershon Kranzler books.
The Secret Code and Other Stories for Boys
Seder in Herlin and Other Stories for Girls
Short adventure story books.
These were among my favorites as a kid.
Cautionary notes: some stories may be mildly scary for little kids.
Recommended
Talks and Tales.
Recommended, if you can find any.
Light.
Recommended, if you can find any.
The Complete Story of Tishrei by Nissan Mindel
Short stories.
Very well-written short stories related to the month of Tishrei.
Cautionary notes: some stories may be mildly scary for little kids, such as the story of Rav Amnon and the writing of Unisaneh Tokef.
Recommended
Chapter book.
Historical fiction
A young Jewish boy joins a group of partisans in WWII.
Cautionary notes: can be frightening for kids.
Recommended
Friedrich by Hans Peter Richter.
Chapter book.
Historical fiction
A young Jewish boy, swept up in the anti-Semitism of WWII, told from the perspective of a non-Jewish friend.
Recommended for older kids.
(the surface has barely been scratched)