August's recommendation: the Odyssey.
You may recall that back in April, I launched my second year of "folklore" or primary source recommendations with the Iliad. We now continue the Classical Year with its companion poem, the Odyssey. See that writeup for a basic overview of how oral epic poetry works, which is useful to understand when you try to read these poems, or listen to them on tape.
The Odyssey is a very episodic story. (In fact, it occurred to me that a game master could use it as a structuring principle for a role-playing game: all the characters are sailors on a ship trying to get home, having adventures on various weird islands.) It's also structured a little oddly: the first four "books" (sections of the poem) are about Odysseus' son Telemachus, who's back at home in Ithaca, trying to deal with the problem of a bunch of suitors hitting on his mom, Penelope. They all think Oydsseus is dead, which is a fair assumption, given that he spends ten years fighting the Trojan War, and another ten getting home. From Telemachus' part we go to Odysseus, who's spent seven of those latter ten years the captive of a nymph named Calypso. Eventually he gets free and ends up telling to the Phaeacians the story of all the things that have happened to him since he left Troy -- cue the flashback.
His journey takes so long because he's not exactly on good terms with Poseidon, the sea-god, which leads to trouble when your way home involves sailing. Some of the adventures he has are familiar to us still: his encounter with the Cyclops Polyphemus, sailing past the Sirens, the bit with Circe and the pigs. Others, like the island of the Laestrygones, haven't remained so popular. Odysseus manages to get all his men killed along the way, but eventually he returns home, where hijinks with disguises and false identites ensue, until Penelope sets up a contest for the suitors, where Odysseus is the only one strong enough to string his old bow. He wins, kills the suitors, kills a bunch of other people for good measure, and finally identifies himself to Penelope. There's one last little coda, often overlooked, where some of the Ithacans want to kill Odysseus for all those deaths, but Athena gets them to reconcile, and all is well.
Like the Iliad, the Odyssey features some of the most nosy and interfering gods you could ever hope not to deal with. Poseidon entertains himself by screwing with Odysseus for ten years, and Athena keeps stepping in to save him and otherwise manipulate events in his favor. It's a problem for any writer who wants to do something based on this story; constant divine intervention doesn't go over so well with today's readers, but without it you're missing a lot of the original story. Still, there have been some retellings. In film and TV, we have a 1997 version, and then looser renditions in Cold Mountain and O Brother, Where Art Thou?. In fiction, aside from classics like Joyce's Ulysses and Tennyson's poem on the same, but then science fiction novels such as R.A. Lafferty's Space Chantey or R.L. Fanthorpe's Negative Minus. Penelope's a popular figure, too, featuring in various poems, short stories, and so on, as well as Margaret Atwood's The Penelopiad. Check out the Wikipedia entry for more titles. Wikipedia also lists, at the present time, nineteen translations; as with the Iliad, I believe Lattimore's is the most famous and widely used.