Odysseus, king of Ithaca encountered the greatest obstacles of all the victors of the Trojan War. For ten years he and his men wandered from place to place unable to return home. (They were turned into pigs by the sorceress Circe; tempted in the land of the Lotus-Eaters and the songs of the Sirens; barely survived the dangers of passing between Scylla and Charybdis, and ran into Polyphemus the one-eyed giant and still survived).
From the travels of Odysseus we can see certain things about the society in which he lived. The men were pretty much allowed to do anything they wanted to do. Odysseus' wife Penelope remained faithful to him all those years even after he was believed to be dead. No one even cared to stop a minute and think if Odysseus was faithful or not. The woman had high expectations put on them but they had no say in the mens lives.
In a way, Odysseus is a great hero because he survived all those trials. Upon arriving home, with the help of his son Telemachus Odysseus killed all of Penelope's suitors, and was reunited with his family at last. A happy ending.
On the other hand, Odyseus was stranded on an island with this beautiful goddess seemingly enjoying himself while his poor wife was at home with the hounding of all her would-be husbands. In the end; in my opinion, Odysseus can't be called all that heroic. He got himself into all that mess, all he did was eventually get himself out of it.