There are a number of benefits to reading the classic works of antiquity. One is simply our natural delight in things beautiful--and there is something truly beautiful about a well-written work. Another is the fact that what passes for a classic work usually achieves that status not only on the merits of the writer as a writer, but on the merits of the writer as a thinker. Classic works deal with grand themes and timeless truths about human nature. As a result of this, for good or ill the works have served as a formative influence on the development of western thought. One simply doesn't understand the modern world as well as he should if he doesn't know how we got here.
For the Christian, perhaps the greatest benefit of reading the ancient classics is the ability to "inhabit" the world of the Bible. Reading the classics helps us to experience the historical and cultural context in which God revealed himself to the prophets and apostles.
I have had the opportunity over the course of the last several years to teach classic literature at the high school level. I am especially fond of the first two years in the four year program. In the first year we read ancient Mesopotamian and Greek works. In the second year we read works from the Roman era. It's a reading course I wish I had had when I was in school. But, alas, with very few exceptions, the emphasis that used to be placed on a classical education has been all but lost.
Here is a list of books I have my students read in the first two years:
Year One: Ancient Mesopotamia and Greece
Epic of Gilgamesh (David Ferry)
Code of Hammurabi
Hesiod's Theogony and Works and Days
Homer's Iliad and Odyssey (Richmond Lattimore)
Sophocles' Theban Trilogy
Bible: Genesis, Exodus, 1 & 2 Samuel, Job
Year Two: Ancient Rome, New Testament, & the Early Church
Livy's Early History of Rome
Suetonius' The Twelve Caesars
Early Christian Writings
Athanasius' One the Incarnation of the Word of God
Historical fiction: Quo Vadis by Henryk Sienkiewicz, a novel about life in Nero's court and the trials of living faithfully as a Christian during his reign
Bible: Luke, Acts, Romans, 1 Corinthians, Revelation