What examples of Greek values are shown in Homer's Odyssey?

There are several Greek values shown in Homer's epic, The Odyssey.

First is the custom of extending hospitality to a guest. This is a rule found in many ancient cultures (e.g., the Anglo Saxons, the Greeks, etc.) and passed down through the ages, and its importance is seen in literature, e.g., Beowulf, Macbeth.

To the ancient Greeks, hospitality was a divine right. The host was expected to make sure the needs of his guests were seen to. 

One of the reasons that Macbeth's murder of Duncan was so shameful in Shakespeare's Macbeth is because Duncan was enjoying Macbeth's hospitality, and so, too, his protection. 

The rules of hospitality also required certain behavior on the part of the guest.

...guests also had responsibilities, beyond reciprocating hospitality.

In the story of Odysseus, the suitors break the rules of behavior expected of guests. They stay much too long, imposing on Penelope, especially in that her husband is not there to force the men to be respectful and take their leave. They waste food, and they are rude to other guests, as well as Telemachus (Odysseus and Penelope's son).

The Greeks would make exceptions for beggars. When Odysseus is dressed as a beggar, Telemachus (at the swineherd's hut) orders his servant to take the disguised Odysseus to the village where he can collect money or food. At his own house, Odysseus is encouraged to beg from the suitors. In the story, Odysseus complains with regard to how he (as the beggar) was treated. This infers that there is an expectation or norm regarding the proper treatment of poor members of society:

[Odysseus] reports that no one in the mansion, not even Telemachus, came to his aid, to defined him, or to punish the offender.

Lastly, the Greek hero is to be admired: he must face challenges and prove himself. He has a responsibility to be respectful of the gods and in their service, display qualities such as strong leadership, wisdom, skill in battle, and honor.

Odysseus breaks this rule when he confronts Polyphemus in Book Nine. He makes fun of the giant Cyclopes and shows a childish side of himself—taunting and teasing his enemy, even after he has won. For this reason, Odysseus is punished.

I was for jeering at the Cyclops again, but the men begged and prayed of me to hold my tongue.

‘Do not,’ they exclaimed, ‘be mad enough to provoke this savage creature further…'

But I would not listen to them, and shouted out to him in my rage…

…Then I said, ‘I wish I could be as sure of killing you outright and sending you down to the house of Hades, as I am that it will take more than Poseidon to cure that eye of yours.’

On this he lifted up his hands …saying, ‘Hear me, great Poseidon… grant that Odysseus may never reach his home alive…'

 …Thus did he pray, and Poseidon heard his prayer. 

Poseidon does punish Odysseus. It will take Odysseus an additional ten years after the end of the Trojan War to find his way home.

Additional Source:

http://books.google.com/books?id=v8AvHMepO8wC&pg=PA475&lpg=PA475&dq=ancient+greece+and+beggars&source=bl&ots=_vGP1HhLHA&sig=O_xvAAJ04PJkt9-MlhASvxCCOG4&hl=en&sa=X&ei=fkDJT4TZDqjW6gHqyOHzDw&ved=0CEoQ6AEwAjgU#v=onepage&q=ancient%20greece%20and%20beggars&f=false

There are, of course, multiple themes within Homer's Odyssey, as it is a very long epic poem. However, there are a few that are more prominent than others:

The first and foremost is the concept of xenia (ξενία, pronounced "zen-EE-uh"), which translates as "guest-friendship." This is the concept of hospitality, which is ruled over by Zeus, showing just how important it was to the ancient Greeks. I have included some links that further explain the concept of xenia not just in the Odyssey, but as a general concept.

Another concept is sophia (σοφία), which translates as "wisdom" or "cleverness." Odysseus is not incredibly strong or skilled like Ajax or Achilles, but he is often described as wily and crafty; the Odyssey is very much about brain over brawn. One example of this is how Odysseus tricks the Cyclops and accomplishes his escape.

A third concept is agalma (ἄγαλμα), which translates as "glory." This is a bit less important than the other two, but it is still there. Odysseus has gained much glory from the Trojan war and his exploits.

The last concept I will talk about is pistos (πιστός), which translates as "trustworthy" or "loyal." One major example of loyalty is Penelope, Odysseus' wife, who holds off her suitors for the entire time Odysseus is gone despite their constant harassing.

These are by no means the only themes within the Odyssey, but they are some of the more important ones.