December's recommendation: the Aeneid, by Publius Vergilius Maro.
In my senior high school English class, I was told that the Iliad and the Odyssey (which composed the other two parts of this year's primary source recommendations) were, like Beowulf and various others, "folk epics" -- as contrasted with the Aeneid, which my teacher called an "art epic." In other words, the former happened "naturally," via oral processes, by authors who are unknown or apocryphal or conglomerate, whereas the latter happened artificially, via writing, by an author verifiably historical.
One could certainly quibble with this simplistic division, but it's true that Virgil (or Vergil; either spelling works) set out to compose an epic in the general style of Homer's much-admired works, and that he did so in a specific political context which very much informs his story. This is something to bear in mind as you read it, as is the general tendency to try and justify one's nation's existence by somehow linking it to Troy. The Aeneid, in brief, tells the tale of Aeneas' departure from Troy after its fall, his subsequent wandering adventures, and finally his arrival in Italy, where he wins a war and eventually becomes the ancestor of the Roman race. (It looks, therefore, something like the Odyssey followed by the Iliad, rather than their usual order.) Along the way, he receives a prophecy that Jupiter has given him "an empire without end," as I believe the phrase goes -- which is the origin of my conviction that the building of Hadrian's Wall (i.e. the end-marker of the empire) was a bad move ideologically, however bright it may have been militarily.
The poem is composed in dactylic hexameter, a specific meter used in Latin poetry; this isn't particularly relevant except that a) it's poetry, so I prefer poetic translations to prose, and b) you might be interested to know that if you recite the Latin text with emphasis on the meter, it sounds very much like you're laying a curse on someone. (I translated parts of the Aeneid in high school, and one of our assignments was to memorize and recite the first eleven lines. I'm enough of a geek that I enjoyed this.) Some of the lines are imperfect dactylic hexameter, though, and the end of the poem's surprisingly abrupt; there's a story that Virgil left orders for the poem to be destroyed after his death, since he hadn't finished revising it yet. Fortunately for us, Augustus (y'know, the emperor) had other ideas. After all, he had encouraged Virgil to write the poem. In light of this, the poem's theme and content become quite understandable.
It isn't all political propaganda, though; there are some great stories within the tale, much like with the Odyssey, such as the nigh-obligatory trip to the underworld. One sequence -- Aeneas' romantic interlude with Dido, the queen of Carthage -- is both an operatic tragedy, and a fine case study in how not to break up with one's girlfriend. It's worth looking at both as an example of a nationalist epic, and as fodder for story material. Also, as a side note, Virgil enjoyed a mystical reputation during the Middle Ages, and people used the Aeneid as a text for divination: select a line or passage at random, read it, and apply it to the situation at hand. For a pagan poem, that's a pretty interesting fate.
At this point, I ought to list off translations and uses of the Aeneid in more popular culture, but I confess to a certain degree of laziness; that's far easier to do for works that haven't enjoyed two thousand years of widespread popularity, and this time Wikipedia doesn't have a convenient list of such that I can use as a starting point. As with the other epics, though, I favor verse translations: if the original was poetry, then so, I believe, should the translation be. We used Fitzgerald in my Latin class, and of course did our own translation; of those two, I would recommend the Fitzgerald.