Odysseus is most certainly a hero. Remember that the true meaning of the term in a literary sense is "main character." Odysseus is not only the main character, but it is also his external and internal conflict which drive the epic poem's action. Even though Odysseus commits several immoral and questionable acts--he is unfaithful to his wife; he demonstrates dangerous arrogance toward Cyclops and in several other events, and he lashes out against the gods--he still develops and changes throughout the poem. He possesses most of the traits of a typical epic hero, such as:
-His father is a king.
-He is larger than life and embodies many of the values of his culture.
-He is almost superhuman (he lives when many of his men die; he seems braver, cleverer, and stronger than most ordinary men).
-He's on a quest (to return home after the Trojan War).
-The divine world interferes with his human world.
-He travels to the Underworld.