The Odyssey is a comic epic poem. Comic in the ancient Greek sense did not refer to humor, rather it referred to the ending, which is harmonious (i.e. Odysseus makes it happily home and all is well). Odysseus is a man who strives to return to his former position as basileus (leader) in his village. The Odyssey is the foil to the Iliad. Whereas in the Iliad the main goal is honor and time, in the Odyssey the main goal is acceptance and harmony. Odysseus uses all the tricks in the book to achieve this goal. It is the story of a man who shows the triumph of right over wrong. Odysseus is the hero, who has restored his oikos (household) to harmony in the face of the suitors, who are breaking xenia.

The important concepts to remember are that back in ancient Greece, the customs were different. They see Odysseus as a hero who restored harmony, not as a murderer who killed 100+ people in his own house.

Edit. Barry Powell provides a good analysis in his textbooks.

Who says he is? Sophocles' Ajax, Virgil's Aeneid, Aristophanes' Wasps (arguably) don't necessarily paint him in a great light, and there are definitely points in the Iliad where he doesn't come off smelling of of roses even in context (Book 9). Shakespeare's Troilus and Cressida doesn't exactly make him off as the coolest guy either. Why he may come off looking better as compared to most of the other heroes is sort of a different topic.

What portrayal are you referring to?

Don't mistake the Greek word "hero" for our word "hero." Originally, a hero wasn't a good guy necessarily, just someone who was larger than life, usually a descendant (however distantly) of one or more of the gods.

Odysseus' role in both epics is summed up in his epithet and in the goddess who patronizes him: he is "Clever Odysseus" and he is favored of Athena, the goddess of (for lack of a better term) strategy, but hated of Poseidon, the patron god of horses, the sea, and (significantly) Troy. But ordinary mortals can, at most, be ordinarily clever; Odysseus is heroically Clever.

As reflected throughout a great deal of their mythology, the Greeks valued intelligence a great deal. Specifically, being "Clever" and using human cleverness to overcome divine and natural elements. Odysseus is a good embodiment of Greek humanism as a whole. He used his intelligence and might to overcome anything that came before him, which are traits that all Greek heroes should hold. The focus of the story isn't so much the specific acts that he did, but how he did them that make him a hero.

In Dante's Divine Comedy, he definitely is not. Dante places Odysseus (or Ulisse) in the 8th ring of the 8th circle of hell, reserved for counselors of fraud, who fit as committers of sins of malice.

For anyone interested in this topic, I would highly, highly recommend checking out the free online course The Ancient Greek Hero led by Prof. Gregory Nagy of Harvard, a world-renowned expert on many things ancient Greece, but especially the idea of the hero. The class includes the Iliad, Odyssey, tragic plays, and many more, and is an extremely interesting, very in-depth, very accessible look at what made someone a hero in Ancient Greece. About a quarter of the class is dedicated to the Odyssey, and of course students are free to participate in as much or as little as they like. Some points from the class that are relevant here:

• The Odyssey is a story about a man (Odysseus) leaving the identity of "warrior" that he had at Troy and reinventing (or even resurrecting) himself as "king, husband, and father" on his return to his palace at Ithica. He was forced to leave those "questionable" things he might have done at Troy (winning Achilles' armour, the rather unsportsmanlike Trojan Horse, etc.) behind him and restore the harmony of his house, as TheSSir said.
• Many ancient Greek heroes acted in extremes - Achilles despoiled the corpse of his rival and even performed human sacrifice, Agamemnon sacrificed his own daughter, Oedipus did what we all know Oedipus did, and so forth - but they were allowed to act in extremes, because the morality under which classical Greeks lived was not a fully-formed entity in what the Greeks conceived of as the "heroic age." Ancient Greek heroes, those who were granted a life after death as "daimones" (supernatural forces, from which our word "demon" comes, but without that word's negative connotations), were seen to ancient Greeks are protectors of the morality under which they themselves lived, but to which the heroes in their lifetimes were not necessarily bound.
• For an excellent and vivid example of Odysseus being seen as not a good guy, see Philostratus' On Heroes (from the Second Sophistic period, during the Roman Empire). That work is relayed as a dialogue between a traveling Phoenician merchant who has been stranded at a port by unfavourable winds and a vinecutter, a man who tends to the sacred garden of the hero Protesilaos, the first Greek warrior to touch Trojan soil, and the first to die there. The spirit (daimon) of Protesilaos is said by the vinecutter to mystically appear to him, using the grove as his exercise grounds, and telling the vinecutter of his experiences during the Trojan War - that is, an "eyewitness" account of the war, better even that the Muse-inspired Homer's poetry. The vinecutter claims that Protesilaos told him that Homer's true source for his account of the War was Odysseus' spirit, conjured from the dead, who in exchange for the information needed to compose the Iliad made Homer promise to paint him in a favourable light. Thus, not only was Odysseus not a good guy, Philostratus even has him poison for all posterity the account of the Trojan War that we still read today.