Why do myths still matter?

Myths function as archetypes of human thought, of the way people perceive themselves as a group and on an individual level, and of the way they view history. They are also the foundations of much of our literature, and as such, they continue to influence our attitudes even if we may not be familiar with the myths themselves and how they came into being.
Though myths influence our perception of history, they are often themselves rooted in historical events which have been overlaid with supernatural actions through human imagination. A good example is the Trojan War. In the late nineteenth century, archaeological discoveries proved that a war had in fact taken place at the site of Homer's Troy. The literary accounts of Homer and Virgil thus represent an amalgam of myth and genuine history. All of this "matters" today because both the Trojan conflict and its offshoot, the founding of Roman civilization by Aeneas, became prototypes of our way of seeing the world dynamic. The Trojan war is symbolic even in our present-day mindset of a struggle between West and East, which many people have exploited as a means of dividing humanity. Similarly, the myth of Aeneas's being tasked by the gods to found a new civilization that will bring peace to the world, as Virgil and the Romans of his time generally believed Rome would do, has been passed down over a 2,000 year period and become the basis for much of Europe's attitude to the rest of the world. We can even more specifically see that the English-speaking world, with its self-conscious ideals of freedom and democracy, has wished to impart English (and later, American) ways of thinking to the world at large.
These effects of mythic stories and symbols are both positive and negative. They have spurred mankind's goodwill but also its darker tendencies in a multitude of cases. But our awareness of myth and its power is necessary to an understanding of history and our contemporary world.