Most of Western Literature, I think, uses biblical allusions, so some stories in particular are crucial to understanding the implications of great literature. To understand Milton's Paradise Lost, for example, you need to know the story of the Fall (Genesis). To appreciate Bunyan's classic allegory Pilgrim's Progress, you need a working understanding of the teachings and assumptions of Christianity, which is most of the New Testament. I can think of few great works of literature that don't allude to or use as metaphors regarding the birth, life, passion, death, and resurrection of Jesus, so you should read the four gospels, as well (Matthew, Mark, Luke, John).
Other classic stories that will pop up unannounced are the story of the Creation (Genesis), Noah's Flood (also in Genesis), and the Egyptian captivity of the Jews, complete with plagues (Exodus).
Other common references--T.S. Eliot springs to mind--are to Psalms and Proverbs.
That should get you started.
The Bible is considered a universal piece of literature and allusions to scripture or the work as a whole are vast. Biblical allusions illustrate how society affects literature and how literature affects and reflects society. A perfect example is early American literature and its reflection of Puritanical values. Because providence was a major tenet of the Puritans, writers would often correlate their daily lives with Biblical events. In her captivity narrative when Mary Rowlandson was spared getting wet in freezing temperatures while crossing a river during her abduction by Indians, she quickly compared her plight with that of "the waters of Babylon" and attributed her safe passage to God.