I've gotten a few messages about reincarnation and how--and if--it relates to Hellenism. Time to talk about it. The idea of reincarnation probably dates back to the Iron Age (so around 1200 BC.). It enters the Hellenic stream of thought and philosophy around the 6th century BC, although there is mention of the theoretical subject in pre-Socratic philosophy.

The ancient Hellenes most likely did not use the word 'reincarnation'; 'Metempsychosis' (μετεμψύχωσις) is a better word for the phenomenon they believed in. It is a philosophical term in the Hellenic language which refers to the transmigration of the soul, especially its reincarnation after death. The notion that the human soul enters another body upon death, though unfamiliar in Hellenic religion, was widespread in Hellenic philosophy. The doctrine of transmigration is first associated with the Pythagoreans and Orphics and was later taught by Plato and Pindar. For the former groups, the soul retained its identity throughout its reincarnations; Plato indicated that souls do not remember their previous experiences. Although Herodotus claims that the Hellenes learned this idea from Egypt, most scholars do not believe it came either from Egypt or from India, but developed independently.

The Orphics were an ancient mystical cult with affinities to Indian religious systems. They believed in reincarnation and the possibility of liberation. Orpheus, the movement's legendary founder, is said to have taught that soul and body are locked together during life; the soul is divine, immortal and aspires to freedom, and during life, the body acts as a prison to the soul. Death releases the soul for a short while, but is then captured by another body until that, too, dies, and so the soul moves from body to body--both human and animal--until it can attain the highest good: liberation. In order to reach liberation, the Orphic way teaches to turn to God by ascetic piety of life and self-purification: the purer the life lived, the higher will be the next reincarnation, until the soul has completed the spiral ascent of destiny to live for ever as God from whom it comes.

As another--less bleak--example, we will look at Plato, who tried to prove the existence of metempsychosis. Plato stated--both in Phaedo and Republic--that reincarnation existed and sought to prove the theory by relating our human rebirth to that of plants and animals: if their souls, their lives, were lost upon death, we would be without them before too long; everything would die out. We are not, however, because out of the deaths of plants most telling, others come up the following year.
Plato believed that the number of souls was finite, so that new ones were not created, and every one transmigrated from one body to the next. In Phaedo, Plato has the following rhetoric to further illustrate the point:

"Whether the souls of men after death are or are not in the world below, is a question which may be argued in this manner: The ancient doctrine of which I have been speaking affirms that they go from this into the other world, and return hither, and are born from the dead. Now if this be true, and the living come from the dead, then our souls must be in the other world, for if not, how could they be born again? And this would be conclusive, if there were any real evidence that the living are only born from the dead; but if there is no evidence of this, then other arguments will have to be adduced. [...] Then let us consider this question, not in relation to man only, but in relation to animals generally, and to plants, and to everything of which there is generation, and the proof will be easier. Are not all things which have opposites generated out of their opposites? I mean such things as good and evil, just and unjust-and there are innumerable other opposites which are generated out of opposites. And I want to show that this holds universally of all opposites; I mean to say, for example, that anything which becomes greater must become greater after being less. [...] Then there is a new way in which we arrive at the inference that the living come from the dead, just as the dead come from the living; and if this is true, then the souls of the dead must be in some place out of which they come again. And this, as I think, has been satisfactorily proved.

[...] I will illustrate by the case of sleep, he replied. You know that if there were no compensation of sleeping and waking, the story of the sleeping Endymion would in the end have no meaning, because all other things would be asleep, too, and he would not be thought of. Or if there were composition only, and no division of substances, then the chaos of Anaxagoras would come again. And in like manner, my dear Cebes, if all things which partook of life were to die, and after they were dead remained in the form of death, and did not come to life again, all would at last die, and nothing would be alive-how could this be otherwise? For if the living spring from any others who are not the dead, and they die, must not all things at last be swallowed up in death? [...] I am confident in the belief that there truly is such a thing as living again, and that the living spring from the dead, and that the souls of the dead are in existence, and that the good souls have a better portion than the evil. [...] Your favorite doctrine, Socrates, that knowledge is simply recollection, if true, also necessarily implies a previous time in which we learned that which we now recollect. But this would be impossible unless our soul was in some place before existing in the human form; here, then, is another argument of the soul's immortality."
He then goes on to have Socrates say the following regarding memories we retain, indicating we do not remember exactly what we knew, but our past lives do influence our loves and abilities:

"If you put a question to a person in a right way, he will give a true answer of himself; but how could he do this unless there were knowledge and right reason already in him? And this is most clearly shown when he is taken to a diagram or to anything of that sort. [...] what is the feeling of lovers when they recognize a lyre, or a garment, or anything else which the beloved has been in the habit of using? Do not they, from knowing the lyre, form in the mind's eye an image of the youth to whom the lyre belongs? And this is recollection: and in the same way anyone who sees Simmias may remember Cebes; and there are endless other things of the same nature. [...] And this sort of thing, he said, is recollection, and is most commonly a process of recovering that which has been forgotten through time and inattention."

Reincarnation is a belief which cuts across diverse cultures of the world today. As a philosophical concept, it is largely a human concept. It is found almost nowhere in religion and mythology, save for one place: the Elysian Fields, which was the final resting place for the souls of heroes and virtuous men. The ancients often distinguished between two such realms--the islands of the Blessed and the Lethean fields of Haides. The Islands of the Blessed were reserved for the heroes of myth. It was an island paradise located in the far western streams of the river Okeanos, and ruled over by the Titan-King Kronos or Rhadamanthys, a son of Zeus. The second Elysium was a netherworld realm, located in the depths of Haides beyond the river Lethe. Its fields were promised to initiates of the Mysteries who had lived a virtuous life. The Gods of the Mysteries associated with the passage of initiates to Elysium after death include Persephone, Iakkhos (the Eleusinian Hermes or Dionysos), Triptolemos, Hekate, Zagreus (the Orphic Dionysos), Melinoe (the Orphic Hekate) and Makaria. When the concept of reincarnation gained currency the two Elysian realms were sometimes tiered--a soul which had thrice won passage to netherworld Elysium, would, with the fourth, be transferred permanently to the Islands of the Blessed to reside with the heroes.

In my personal practice, I make a clear distinction between religion (as represented by mythology) and philosophy. I feel myth was inspired by the Theoi Themselves, while philosophy was created by humans who saw society and drew conclusions from it. These conclusions often included a religious aspect because society was religious (even though the ancient Hellenes didn't have a word for 'religion'), but at its core, they deal not with religious matters. They deal with the influence of religion on humanity and society. As such, philosophy--of which I am a great fan, by the way--will never be the foundation of my faith, because religion and philosophy have a different goal; one to guide mankind in the way of the Theoi, the other to understand mankind. There is nothing religious about the latter although it can greatly influence your religious practice.

The belief in reincarnation--or perhaps better, metempsychosis--existed in ancient Hellas and was wide-spread in one form or another. Just like today, mankind sought to relieve the fear of death and the belief in a second chance at life was a popular way to accomplish this. Where you stand on the subject is entirely up to you.