The word epic has been subjected to such wholesale misuse by teenagers and video gamers over the last few years that for many its original glory has been lost, along with its actual meaning. It doesn't refer to doing a sweet jump on your skateboard, pulling a prank on your best friend, or beating everyone in your class on Halo.
An epic is a long tale describing culturally significant events. Originally all epics were verse narratives, and the earliest ones included creation stories, tales of man's origins, anecdotes about the gods, and chronicles of war and conquest. Eventually epics were written in a variety of forms (poetry, prose, film), and shifted away from stories of beginnings to a more contemporary focus. The Russians became particularly good at this latter form, with books like War and Peace, And Quiet Flows the Don, and The Brothers Karamazov ranking not only as great epics, but among the greatest literature.
Epics are, by definition, universal. While each one is culture-specific in its details and conception, each one also attempts to gauge and explain man's nature and the world he's made (and which in turn makes him). Virgil's Aeneid is ostensibly about the creation of Rome, but it goes much deeper; ultimately, it's a meditation on the foundations of political authority and human power.
More culture-specific, sagas are simply prose epics originating in Iceland, Scandinavia, or from among the Germanic tribes. They tend to be even bloodier than most of their counterparts (The Iliad is a notable exception), though often also more Christian. The sagas were written after the Christianization of Northern Europe, and while many pagan ideas persisted, there was a move among the literati to infuse Christian ideas and imagery in their stories, even those that originated before the coming of the first missionaries.
One of the distinguishing elements of epic and saga is each story's scope. Something like Sir Gawain and the Green Knight is romance rather than epic because it's so personal; we aren't hearing about earth-shattering or kingdom-defining events, we're getting an intimate look at, and (more importantly), inside a man who is in many ways simply the pawn of kings. Epics, on the other hand, are about the kings themselves, or at least those closest to them, their generals, their advisors, their betrayers.
At the same time, there is a personal element to epics, even the most impersonal ones. The Odyssey is about one man's difficult journey home after years at war. He longs to be reunited with his wife Penelope, and Odysseus/Ulysses faces nearly insurmountable odds to realize that goal. This is the aspect of epic that has led some critics to suggest a novel like Huckleberry Finn can be read as an epic.
However you categorize your favorite novels, epics are the forebears of pretty much any great work of fiction we read today. To present the life of kingdoms through the lives of their heroes was a literary innovation writers haven't been able to abandon since some brilliant Sumerian recorded the adventures of Gilgamesh for posterity. And, in the very spirit of epics themselves, we count ourselves (along with any others who've read it) among the posterity for which he wrote.