Many Neo-Pagans were awakened to the old gods by an early encounter with Greek mythology, yet now they follow other traditions. In this paper I will try to clarify several issues that may deter Neo-Pagans from the Hellenic path.
A connection with the Earth is an essential part of Paganism, both Neo- and Paleo-, and thus many Neo-Pagans look to their ethnic roots as a source of spirituality, but I think that ethnicity can be construed too narrowly. It's a mistake to reject the Hellenic path simply because you're not of Greek descent.
Hellenic culture is a major component of the substratum of all European culture. It is worth recalling that by 327 BCE Alexander had carried Hellenic culture nearly to the Ganges and to the north of the Himalayas (and, of course, brought Eastern culture back to Greece, for his goal was a multi-ethnic society). The conquest of Greece by Rome was complete by 146 BCE, but in its defeat Greek culture conquered the Romans. It then spread with the Roman Empire, which by 44 BCE included the North African coast and extended north to the English channel; by 67 CE it included the south of England. Therefore the Hellenic tradition has been a part of the culture of Europe (and beyond) for at least 2000 years. To the extent that European culture has become Western culture, and Western culture has become world culture, the Hellenic tradition is ubiquitous. As Shelley quite rightly said, "We are all Greeks" (Preface to "Hellas").
In particular, the Greek gods have never been far from the center of Western culture, and Greek mythology, more than other Pagan traditions, continues to be a major influence in literature, art and language. For these reasons, I think it is accurate to say that the Greek gods are the gods of Western culture, wherever it exists in the world, and therefore that these gods are part of the ethnic background of everyone who feels Western in this sense, no matter what their race or geographic origin. (I hope it's unnecessary to say that I'm not claiming the superiority of Hellenic or Western culture; my point is only that the Greek pantheon is a natural choice for anyone at homtern culture.)
Once freed from an overly-narrow idea of ethnicity, one sees that the Hellenic tradition has much to offer. Although the gods can be known through many different pantheons, there are practical differences between them.
For example, since the Hellenic tradition stretches continuously from before Homer's time (say, 700 BCE), through the Christian era, to the present, there is a larger surviving body of literature, artifacts, history, art and religion from the Hellenic tradition than from any other Western Pagan tradition. Therefore there is a much more solid basis for constructing a Hellenic Neo-Paganism than for the other traditions. The large corpus of surviving texts and the enormous body of scholarship makes reconstruction easier in the Hellenic tradition than in others, such as the Druid or Wiccan, which have been reconstructed from a few shards of evidence or undocumentable oral tradition. Although these reconstructions may be very good, in the Hellenic tradition we have a better chance of understanding archaic thought, so that we can make informed decisions about what we accept or reject. With many of the others traditions it's nearly impossible to distinguish a practice tested for a hundred generations from one cooked up last week by someone who has just read The Golden Bough (or The White Goddess). The gods are living, and new traditions must be created, but it's also important to understand how They were worshipped in the old days.
The wealth of source material makes the Greek gods much more knowable as personalities. For me at least, the Germanic gods are still largely cardboard characters, and the Celtic gods are little more than a jumble of names. I also realize that the understanding I do have of the Germanic gods has been formed as much by Wagner as by the Eddas and it has been observed that Wagner's gods are really just the Greek gods with German names! I think it's crucial to know the gods personally - intellectual understanding is not enough - and the way to Them is opened by a large corpus of myth, art, etc.
Of course, a practical disadvantage of the Hellenic path is that it's a comparatively small tradition in contemporary Neo-Paganism, so there are fewer organizations, periodicals, practical books and group activities (though I hope the recent institution of the Nashville Panathenaia signals a new trend). I don't know why Hellenic Neo-Paganism is less popular (you tell me!), but one reason may be that the very familiarity of the Greek gods robs them of the novelty of the Celtic, Wiccan, and other traditions.
Next I'll discuss somteristics of Hellenic Paganism.
The Hellenic religion is sometimes criticized for being patriarchal, but to me it doesn't seem any more patriarchal than other ancient religions. (Of course, the society of Greek mortals was enormously patriarchal; the Romans were less so; the Etruscans less yet.) Zeus's supreme position is really only nominal; He frequently gives in to other gods and goddesses. All the gods, or at least the twelve Olympians, are very nearly equal in power. Indeed Zeus got his job by means of Rhea's carefully laid plans, witlp of Gaia! In a sense He is Their instrument.
In ancient times the immortal males and females had nearly equal power and respect. Observe also that the twelve Olympians are balanced in gender:
Hera, Poseidon, Athena, Aphrodite, Apollo, Hermes,
Zeus, Demeter, Hephaistos, Ares, Artemis, Hestia;
six and six. As part of the transition to the Piscean age Hestia gave her position among The Twelve to Dionysos (a god of ambiguous gender), but Hestia was not demoted; She is the oldest Olympian, and still foremost in Their company.
In terms of ritual, the Greeks and Romans respected the goddesses as much as the gods, and most of the public religious festivals were devoted to goddesses concerned with the cycles of nature and other "earthy" things. In addition, out of the 33 surviving "Homeric" Hymns, 17 are to gods, 15 to goddesses, and 1 to both (Apolhe Muses) - approximately 50-50.
Sometimes the Greek gods are ridiculed for their immorality, but I think this betrays a misunderstanding of divinity. The gods are not moral ideals.
Nobody would suppose they would make themselves a better person by emulating Zeus, or even Athena or Apollo (let alone Hermes or Pan). (Indeed, aspiring to be like the gods is the most obvious form of hubris, and invites Their wrath, as we see from many myths.) But this does not mean the gods are immoral. The gods have Their own morality, and it makes no more sense to apply Their moral norms to us, than it would to apply our moral norms to wolves. Gods, people and beasts are three different classes of beings, each with their appropriate morality (though there may be some overlap). For example, gods may engage in incest, perhaps to achieve some aim, such as begetting a new god with a specific character, and there is no reason to suppose that such incest would have any of the disastrous genetic and psychological consequences that it does for people. Gods are different, both genetically and psychologically, from people.
Therefore I think that the object of knowing the gods better is not to become more godlike, but to better comprehend Their will so that we don't oppose it, and if possible to enlist Their aid in our activities, both magical and mundane.
We worship the gods - we respect Them, acknowledge Them - because They are the ineluctable powers of the universe, neither good nor evil (because our moral categories are not appropriate for Them). For me the gods are the ultimate necessities of the universe, and hubris is a failure to abide by these necessities. As Philip Vellacott says, "The nature of a god is not to be man's friend, nor man's enemy, nor man's moral guide. It is the Hebrew and Christian tradition that presents God as embodying what ought to be, the ideal; the Greek god is the opposite of this, and stands for 'what is' - in human nature, in humay, and in the universe."
Which brings me to my last point, concerning the quarrels and deceptions of the gods. Naturally we put these things into our own terms, but I think that the myths reflect actual conflicts between these ineluctable forces. Personally I find the universe much more comprehensible when global and personal history is viewed as partially the consequence of interacting gods - sometimes working together, sometimes opposing one another, more often just going Their own ways, with the inevitable collisions. (In other words: if this world is the orderly unfolding of the Master Plan of One God, then He or She must be schizophrenic!)
Concretely, recognizing the many gods and Their conflicting demands can lead to a healthier, happier, more balanced life. Consider the myth of the Judgement of Paris. He finds himself in a common enough situation: three goddesses demand his attention. Poor Paris tries to avoid making the decision, but They will not let him off. In the traditional story he is offered kingship, heroism and love, but we may interpret the bribes as wealth, wisdom and love (still in our day, frequently, mutually exclusive choices). He gives the golden apple (inscribed "for the most attractive") to Aphrodite, and the result is disaster - the Trojan War. But his mistake was not that he gave the apple to the goddess of love, for She is a goddess nonetheless. Rather, Paris's mistake was that he slighted the other two goddesses. Had he given the apple to Athena or Hera, the consequences would have been just as bad (although perhaps quite different in detail).
How could Paris have escaped this trilemma? That's difficult to say, but he should have tried to respect the sovereignty of all three goddesses. Perhaps he could have convinced Them to share the apple, each possessing it for a time, since at some times wisdom is most desirable, and at others power, and at yet others, love. Or he might have made propitiatory sacrifices to the losers. Perhaps it was simply a "no win situation" - the Romans would say he was "between axe and altar."
It's characteristic of polytheism to confront such situations head on. There is no supposition that there must be a single Right Way, if only we could find it; polytheism acknowledges that sometimes there is no right answer. We must often make irrevocable decisions, honoring one god but dishonoring another, and we must pay the price to the offended gods, in spite of the fact that we couldn't avoid offending them. Luckily we often have options (analogous to dividing the apple) that were not available to Paris, which may mitigate the consequences. But I think polytheism forces us to acknowledge that sometimes there just isn't a Right Way.
How much more clearly we understand the world when we see that Hera, Aphrodite and Athena all have their demands! We don't fret over which is "God's Will" when we see that there are three goddesses, each with Her own will. If we decide that only one demand is the true "will of God," then we obey one goddess at the expense of disobeying the others - to our own sorrow! Although Paris may have been in a "no win situation," he made the outcome worse by rejecting Hera and Athena. Unlike the Christian god, who proclaims His jealousy, the Olympian gods do not mind other gods being recognized. What They do mind is being rejected, and that They punish.
Is it good or fair for gods to put mere mortals in such predicaments? No, but why suppose the - by our standards - good or fair?
Greek religion is very different from Christianity in that the gods don't care at all what you believe, so long as you worship Them. They demand cultus (from the same root as "cultivate") - tending the sacrificial fires, remembering Them - and one purpose of prayer and ritual is to nourish the gods and so rejuvinate them. The Greeks were quite explicit about this; a god could be hungry for the fragrance of the sacrificial fires. Then as now you can even be an atheist, so long as you recognize the gods and conform to Their will. Conversely, all the piety and faith in the world will not save you if you do not obey Their will. Greeks felt free to choose what they might believe, and so the Christian church fathers rightly called Hellenism the "father of all heresies" (from hairesis, choice).Greek religion is a matter of orthopraxy (right doing) as opposed to orthodoxy (right saying).
The point is that the gods reward behavior in accord with their will, and punish behavior not in accord, regardless of whether you believe in Them or not. Of course, if you believe in Them, you are more likely to know Their will and act accordingly, but there are no guarantees either way. An unbeliever may by chance do the right things; conversely a believer may misinterpret Their will, and act wrongly. However, wisdom and undersis more likely to result in right action.
One of the most informative discussions of the spirit of Greek religion is Walter F. Otto's Homeric Gods (Pantheon, 1954); he was a Neo-Pagan in attitude if not in fact. Other sympathetic surveys are Thaddeus Zielinski's Religion of Ancient Greece (Ares, 1975), which must be read critically, and Charles Seltman's Twelve Olympians (Crowell Co., 1960; orig. prod. by Pan Books Ltd). Walter Burkert's Greek Religion (Harvard, 1985) is a good, reasonably up-to-date survey of Greek religious belief. For an insightful retelling of the myths I recommend Carl Kerenyi's Gods of the Greeks (Thames & Hudson, 1951), which has a Jungian slant, but has excellent citations for the sources of the myths.