I also recommend A Cricket in Times Square by George Selden, the Amelia Bedelia books and the Boxcar children.

As a child I reread these books a lot (I listed them in random order), but since it's been awhile I may not remember if there's scary or mature content:

A Little Princess by Frances Hodgson Burnett
Little Women and Eight Cousins by Louisa May Alcott
The Black Stallion (and some of the series) by Walter Farley
Heidi by Johanna Spyri
The Secret Garden by Frances Hodgson Burnett
The Little Prince by Antoine de Saint-Exup�ry