From a literary perspective, there is very little the Greeks did not invent. Philosophy, politics, and science on the one hand, and drama, poetry, and novels on the other—while all these genres may not have originated in ancient Greece, they were certainly perfected there. Immanuel Kant and Georg Hegel may have thought history was an endless progress, but their intricate tracts were no improvement on Aristotle or Plato; and while Shakespeare may have found new ways of expressing human emotion, he lifted many of his plots freely from those of the Greek tragedians.
The Preacher of Ecclesiastes said there is nothing new under the sun. The history of literature since the Greek era certainly supports this claim. While modern critics make a big show of disagreeing with Aristotle's art theory, the fact is they're still responding to his ideas more than two millennia later, making their supposed originality a debatable point. Plato's Republic is still cited in discussions of government and political theory; Oedipus Rex is still one of the best examples of a tragedy; almost any well-read person has read The Iliad and The Odyssey.
In Poetics (the first known example of literary criticism), Aristotle identifies a number of elements every work needs to be considered good or satisfactory. He deals with drama, contending that a good playwright observes the unities (action takes place through the course of a single day in a single place), that tragedy is superior to comedy, and that dialogue should reflect the attitudes and morals of the characters. Perhaps his most important (and controversial) ideas, however, concerned the purpose of art.
Art has the power to affect both the emotions and the intellect. Aristotle identified the mission of all good art as twofold: to delight and instruct (on an intellectual level), and to provide catharsis (on an emotional level). To delight, art must be aesthetically pleasing, meaning that its individual elements should cohere, its message should be consistent, and it should present whatever ideas the author intends with style and grace. To instruct, art must include an underlying message (or messages) that the audience can identify and that will fuel thought and (ideally) action.
Catharsis is more personal and more complicated. A good poem or play or novel should cause the reader or listener to purge negative emotion through projecting them on the characters encountered in the work. People are naturally disposed to negative behavior, but a good play can help them experience vicariously acts they would ordinarily commit on their own. All these elements of art are capable of moderating and bettering society, as long as the artists wield their influence properly.
Perhaps the reason we still read Homer and Euripides and Aristophanes is that each of them managed to delight, instruct, and provide positive catharsis that still speaks to the universal human condition. Of course, Greek thinkers were not united in this evaluation: Plato suggested that poets were pernicious, and should be cast from the midst of a perfect society, along with their works. But his was the minority opinion, and most Greeks recognized the power of the written word to shape men's thoughts and lives toward the ideal of human virtue.
On the other hand, much of Greek literature represents a distinctly humanist worldview, one built on the principles of virtue as simple public obligation, the promotion of man above God (or, in the Greek case, the gods), and the use of reason as the ultimate rule for the attainment of perfection. The Christian view is quite different, built as it is around total reliance on God. And yet, Christians have much to learn from the ideas of Aristotle and many of his fellow Greeks concerning art: that it can be a positive force, that art (particularly literature) does affect each of us, and that poems and novels should project ideas rather than merely provide dumb entertainment.