I'm about three-quarters done with Homer's Odyssey, and I have a couple of thoughts:
:: First, I suspect that for many people, when you mention The Odyssey, they think of Odysseus lost at sea and having all manner of amazing adventures – the Cyclops, Scylla and Charybdis, the Lotus Eaters, and all the rest of it. Having reached the point in the book where Odysseus returns to Ithaca, but under disguise, I am struck by how little of the book is actually about all those adventures that constitute the most famous part of the story.
:: Second, the non-linear structure of the story surprised me a bit. Here my expectations were undoubtedly colored by the "simplified" version of Odysseus's adventures way back in seventh grade, but I sort of expected the book to open with Odysseus leaving the shores of Ilium and then having all manner of difficulties on his way back to Ithaca. However, Homer's actual telling of The Odyssey is decidedly different: it actually doesn't begin with Odysseus at all, but rather with Telemachus, his son, who despairs of his father's return as a group of suitors gathers around Penelope, looking to carve up Odysseus's estate among themselves.
Thus I expected to start with Odysseus and follow his exploits on the way home, but instead the book begins with him already missing. Rather than a straightforward adventure story, the Odyssey begins as a mystery, a "missing persons" story. We follow Telemachus as he embarks on his own journey to search for his father, which has the further purpose of letting us learn how the war on Troy ended after the death of Hector at the end of The Iliad. Telemachus goes to the courts of Nestor and Menelaus, hears stories of his father's exploits; we learn about the hardships suffered by all of the victorious Achaeans on their journeys home, before we finally join Odysseus in Book Five, as he is held captive by Calypso.
:: Third: repetition of motifs and verbal cues. There's a lot of this in The Odyssey, whereas I didn't notice nearly as much recurrence in The Iliad. The best example is that, whenever a day begins in The Odyssey, Homer uses a line like "When Dawn with her red fingers rose once more…." And in Book VIII, "A Day for Songs and Contests", Odysseus is twice moved to tears by the proceedings at the great feast in the Phaeacian court; both times he casts his cloak over his face, seeking to conceal his tears, and both times Alcinous – who, in fact, later saves Odysseus by providing him a ship to take him back to Ithaca – is the only one to notice Odysseus's tears and intercedes to lighten the mood. The repetitions seem, to me, to more reflect the poem's legendary oral genesis, even though it is far from certain to what degree the poem, as we now have it, springs from a tradition of oral performance.
:: Fourth: I haven't come yet to when Odysseus literally cleans house and kills all the suitors, but it's pretty obvious. What a delicious bunch of villains they are; I can only imagine Greek audiences, hearing the poem in whatever manner it was performed, hissing at their mere mention.
:: Fifth: I think that a Peter Jackson-directed version of The Odyssey would be a pretty nifty movie.
:: Finally, reading these books sort of makes me understand why Greece converted to Christianity. I imagine they were pretty relieved: "Whoa, you mean, we don't have to believe in those guys anymore?" asked while jerking a thumb at Mount Olympus. These Gods are a pretty creepy bunch.