To begin, both the encounter with the Cyclops and that with the Lotus-eaters serve as episodes in a journey that takes Odysseus away from Troy and far from the realms of Greek civilization. In this respect, the entire story he tells the Phaecians is emblematic of Greek notions of heroism,...
To begin, both the encounter with the Cyclops and that with the Lotus-eaters serve as episodes in a journey that takes Odysseus away from Troy and far from the realms of Greek civilization. In this respect, the entire story he tells the Phaecians is emblematic of Greek notions of heroism, bound up as it is in this larger voyage filled with extraordinary struggles, triumphs, and sorrows. He's a very larger-than-life kind of personality, and that is a central trait to any classical hero.
Favoritethings has already addressed the question of the Lotus-eaters. To this I would only add that in The Odyssey, Odysseus stresses his own personal role in bringing the crewmen back with him; he doesn't delegate it to others. He takes on responsibility for them and then gives the order to leave the island. Odysseus is active rather than reactive and does not shy away from the challenges which face him.
His encounter with Polyphemus is one of the most famous incidents in the poem, and an episode that illustrates Odysseus's cunning and ingenuity in how he out-thinks and outmaneuvers a far more powerful opponent. In this alone, he embodies traits of the hero. On the other hand, to contemporary audiences, certain elements of this encounter can be problematic. Take, for example, his final decision to give Polyphemus his name. From a modern perspective, this is pure arrogance: pride overcomes good sense, to disastrous effect. On the other hand, when addressing a question such as yours, you should consider how cultural norms evolve over time, as what was considered heroic by Ancient Greek standards won't necessarily reflect what is considered heroic today. In any case, classical heroes tend to reflect larger-than-life personalities and accomplishments, suspended somewhere between the realm of humans and the realm of gods. Even when Odysseus makes this gross error in judgment, acting purely out of ego, he might still be living up to the heroic literature. Odysseus wants to make his achievement known, and he wants Polyphemus to know who it was that defeated him.