Odysseus' bow (symbol)
The mighty bow of Odysseus, which only he can string, is a symbol of his rightful place as king of Ithaca and husband of Penelope. By stringing it after all others have failed, he asserts his dominion and proves to the suitors that their efforts to take his wife and land from him have been in vain.
Odysseus' dog, Argos (symbol)
Aside from being one of the most memorable and sympathetic figures in the poem, Argos can also be seen as a symbol for the fidelity of Odysseus' household in his absence. The implication is that Argos could not die until his master returned, out of unparalleled loyalty to him; just so, Penelope and Telemachus stayed loyal to Odysseus in his extended absence, despite the many efforts of the suitors to dissuade them from this loyalty.
Hospitality (motif)
A motif representative of ancient Greek culture is the willingness with which households took in strangers, clothed them, and fed them, prior to asking who they were or what their business was. This same kind of generally welcoming attitude is what undid Odysseus in combination with his hubris, when he demanded a guest-gift of Polyphemus, who had no intention or cultural obligation to give him any such things; thus began the chain of events that kept Odysseus from his homeland for so long.
The Transfiguration of Odysseus' men by Circe (allegory)
When Circe transforms Odysseus' men into pigs, a possible allegorical reading invites itself: because the men blindly surrendered to Circe and gorged themselves like pigs, the transformation was as much reflective of their true nature as it was wicked magic on Circe's part.
The final journey of Odysseus (symbol)
Tiresias' charge for Odysseus to complete his journey by traveling inland with an oar until he reaches a people who would mistake it for a winnowing fan, at which point he must bury the oar and sacrifice to Poseidon, is a symbol somewhat resistant to explanation. One promising interpretation is that Odysseus cannot make peace with the deep agonies he suffered on his journey home until he has moved on from them in mind and body, as symbolized by traveling to a land that knows nothing of the sea: only then can he reconcile with himself and with the gods.
