As far as story Bibles go--and we have many--our absolute favorite is The Child's Story Bible, by Catherine F. Vos. Published in 1935, this 700 page volume was recommended to us by Carole Joy Seid and has not disappointed. Vos accurately weaves the words of Scripture with historical descriptions of the sights, sounds, and smells surrounding the people of God. She goes beyond mere narration to explain the attitudes and emotions that come with both the circumstances and choices of these people of old. The Bible's "mature issues" are dealt with tactfully without lessening the impact of the subjects themselves. Reading a few of The Child's Story Bible's short chapters per week is a great way to take even the squirmiest of children through the Bible in a year.
Another delightful book is A Little Life of Jesus For Children Who Are Learning to Love Him, by Lois Rock. This chubby little book, perfect for toddler sized hands, had accompanied us to church for many years and is still kept lovingly by the bed of my five-year-old. The simple stories of the life of Christ taken from the Gospels are illustrated by eye-catching pictures on every page. Sadly, it seems to be out of print in the U.S. and I don't know of any American retailers who carry it. I've seen it on Ebay and Amazon used, and if you can get one, do so.
Finally, a worthwhile newcomer to the plethora of story books on the shelves of your local Christian retailer is The Jesus Storybook Bible, by Sally Lloyd-Jones. Lloyd-Jones does a marvelous job of taking all the major stories of Scripture and shooting them like well-aimed arrows at the target of the Messiah. The redemption story is central on every page. And I especially like the illustrations--Abraham, Moses, and Jesus actually look Middle Eastern! While we don't own it yet, our pastor is reading it a chapter at a time to the children on Sunday mornings and it is quickly becoming a favorite.