One that has already been mentioned is that of Moderation, or keeping to the Mean or the Middle Path. This is, not in itself unique to Hellenismos. One of the Confucian Classics is the Great Mean, and Chinese philosophy traditionally also valued Té or Virtue, (often divided into Five Cardinal Virtues as well); while Buddhism also valued the Middle Path as well.
Eusebia (piety) has been mentioned in the discussion of virtues as one possible Fifth Cardinal Virtue. Like the other virtues, the Hellenes viewed eusebia as a mean between two extremes. At one extreme was aesebia or impiety, which in essence meant failure to participate in or perform the traditional rituals of worship to the Gods, Demigods, Nature Spirits, Heroes and Ancestors. These were usually public rituals, done by the community or the locality or the clan. Rarely was belief contrary to the accepted tradition criticized. Anaxagoras and Socrates both were put on trial by Athens for their teachings. Socrates was also satirized savagly by Aristophanes in The Clouds.
On the other hnad, at the other extreme was excessive piety, which came in for as much criticism as insufficient piety. Those who spent too much time fearing the Gods, or worrying that something they had done had offended the Gods, or spent all their free time praying at the altars, or attending to the divine images constantly, adjusting the offered peploi and the like led some to make the witty remark that "the Gods do not need bodyservants." This excessive devotion or fear was derided as deisidaimonia, literally "fear of the spirits (or Gods)" which meant, and is translated as superstition (via the Latin equivalent term of superstitio.
So one should be mindful of the Gods and their gifts, and make the appropriate prayers and propitiations. But one should not abase oneself (which is why one stands when praying, rather than kneeling). The relationship with the Gods is not one of ignoring or denying them, nor is it one of excessive and slavish abasement and adoration. One stands in relation to the Gods as a free person, dealing with a free person of higher status.
Another value of great importance was the related values of Timé, Kléos (Honor and Fame) and Aidos (Shame).
The film, Troy did get the desire for fame very well. One tried to do acts that would be remembered by the community and others. The warriors at Troy, to the extent that one believes they existed have won fame that has lasted three thousand years. In the ancient world, people still came, as late as the time of the Emperor Julian to the Tombs and Shrines of those heroes. Even now, people visit (W)Ilios in large part of the enduring fame of Akhilleus, Odysseus, Hektor, Aineas, Agammemnon and the others. Successful people were rewarded by poems in their memory, statues erected by their cities and the like. This classical value still persists in some areas strongly influenced by classical civilization. To this day, if you ask Latin Americans (males, primarily) if they'd rather be written into the Empyrean Lamb's Book of Life or have a street named after them, or a statue erected to them in Central Park, they will, almost without fail, seek Kléos and Timé over Christian Salvation, if forced to make the choice. How do they seek to gain these statues and fame? By excellence in their actions, demonstrating skill, bravery, etc.
Honor was also an important value. By doing great deeds that helped the community, not only did they win memories for themselves, but also win honors. Until recently, with the rise of individualistic and internalized ethics, honor was not something internal. We can console ourselves today that we acted with honor. And I'm sure to an extent, an ancient Greek could console himself in that manner. But in essense, honor is something granted by the community. It is community recognition for one's actions and accomplishments and skills. Over and over again, I would read how one sought honors from the community so they could claim honor. Growing up in our internalized guilt-oriented modern world this made no sense, until I examined other modern socieities. Once again, my Latino heritage explained it via a survival of classical values there, and I confirmed this by other studies of the ancient world.
Ancient Greece was an honor-shame society, much as modern Italy, Sicily, Spain and Latin America are (as is China, Japan and the Middle East). Honor is granted by society, and so one is considered honored by the honors granted by one's community and one's peers. One is jealous of the honor one gains, as one may lose it based on community reactions. In more modern sense, to lose honor is to lose face. Certain types of action are considered as acting with honor, and society recognizes that and says you have honor, often giving a title.
Hence Akhilleus' negatie reaction to the claim of Agamemnon to Briseis, espcially as it was done in front of the army entire. He lost face by that action, and Agamemnon's claim that the army did not need the courage and skill (andreia) of Akhilleus. So Akhilleus sulked in his tent for being dishonored. We normally think of Akhilleus as acting childishly here. But he wasn't. He states his intention to go on strike and prove how the army needs him, to restore his honor in the eyes of the army, and to have it restored to him publicly. He plans on shaming Agamemnon, and he eventually succeeds. Without Akhilleus, not only can the Akhaiwoi army fail to conquer Wilios, it can hardly defend its own ships.
Aidos, or shame, is also a public thing, granted by the public. People shame you, or expect you to feel shame by their reaction to you. One is then ashamed, and not honored. Rather than an internal (guilt) response, it is a public response often resulting in ostracism and shunning. In Spanish there is the phrase "sin vergüernza" (without shame). To be without shame, or shameless is a bad thing, as a lack of shame means you don't care what others think and will act in a socially negative manner. Its as if one is guiltless despite of how one acts, i.e., a sociopath.
So the overall effect is to encourage people to engage in socially positive manners, and so gain Timé and avoid socially negative manners and so avoid accumulating excessive aidos or shame.
The last major value that Hellenic society preferred value is Xenia or hospitality. One was expected to offer hospitality (food, drink, shelter) to suppliants (beggars or prisoners), strangers and the like. Offering hospitality created a bond with one's guest. The guest was expected to behave, and treat the host well, and the host had to treat the guest well, and protect the host. It formed a sacred bond of guest-friendship, as the guest was obligated to reciprocate if the host ever needed anything.
The most dramatic form of this hospitality came in the ritual of hekatitia. If someone grasped one's knees in supplication, one had to provide protection to this supplicant. Usually this was someone you had bested in battle. It meant one had a duty to protect the person until they were ransomed (if a prisoner). Less extreme versions were more common.
Failure to provide shelter, or protection could be very bad. If one broke the bonds of guest-friendship, by stealing from or abusing one's host, one had broken a key bond of society, and became an outcast. Paris violated this bond seriously by stealing Menelaos' wife, Helen, and sparked a war. The suitors were poor guests, and paid for it with their lives when Odysseus returned to Ithaka. On the other hand, poor hosts, such as the Kuklopes could be harmed by their guests in retaliation.
Failure to respect Hekatitia or supplicants could also be very serious. Agamemnon fails to respond properly to Khryses' petition to return his captive daughter. As a result of the abuse Agamemnon heaps on the old priest, Apollon punishes the Akhaian camp. When Akhilleus refuses to honor the hekatitia a Trojan prince performs on the banks of the Scamander river, the River God attacks Akhilleus to punish his inhospitality and pride. On the other hand, when Priam comes to ask for the body of Hektor, Akhilleus receives the old King graciously and with the proper respect for a suppliant and returns the body. (The Iliad opens with Agamemnon's inhospitality, and closes with Akhilleus' hospitality a neat contrast; much as the Odyssey contrasts the poor hosts, the Kuklopes with the good hosts, of Scheria, the good guests of Odysseus's men versus the poor guests of the suitors).
Thus we can see the importance placed on piety, honor, shame, glory/fame and hospitality in ancient Hellas. We can also see how moral lessons were contained in the Epic poems of Homer which serve as exemplars and cautionary tales.