The Denver Post has a nice story summing up the religious undercurrents of the upcoming Chronicles of Narnia movie. I read and enjoyed all the books in elementary school and was completely oblivious to the religious allegory in them (despite having a Christian upbringing). Narnia is not the Veggie Tales (a children's series which is quite transparently comprised of Chrisitian allegory).
I also read the Lord of the Rings books (well, actually, I stalled part way through the Two Towers and then watched the movies when they came out), which are considerably darker than the Narnia series and aimed at an older audience. Their links to Christianity are far more ephemeral.
The lives of the authors is well documented. C.S. Lewis, the author of the Narnia series, was a Christian apologist whose work is still regularly read by Chrisitans in Denver today (I know a couple that met in a C.S. Lewis book group and went on to marry), and is still regularly cited in sermons. The non-Narnia part of the world draws very directly from his experiences in World War II (when he took in children fleeing the London blitz at his country estate).
Tolkien's work probably owes more to World Wars I and II, than to any Biblical epic, and also shows a striking familiarity with the scourge that is addition to drugs or alcohol, although I'm not familiar with any biographical data discussing Tolkien's familiarity with the later theme in his personal life. The two authors certainly knew and influenced each other.
Perhaps, we'd be better if we had Narnia but not the Bible. The Narnia books have worthwhile messages, but they don't pretend to be anything but fiction. As a result they tend to do more good than harm. The other literary collection called the Bible doesn't have such a good track record for doing the same.