As an example of how the stories are not identical, consider the myth of Prometheus that Shawn10538 referred to in an earlier post as nothing else than the Christ story:
[I]f you take the Christian elements out of the ancient myths, there would be no story left. The central theme of Prometheus (a work that we have complete copies of that date before Christ) is that the Son of God was born of a virgin, saved mankind by revealing fire to them, died crucified, and was resurrected (in Prometheus Unbound). that IS the Christ story, it's not just a story with Christian elements. And that is just one example.
Have the parallels been exaggerated? The two main pre-Christian versions of the Prometheus myth are those of Hesoid and Aeschylus and these are available online for anyone who wants to examine them (cf. http://classics.mit.edu/Browse/browse-Hesiod.html and http://classics.mit.edu/Aeschylus/prometheus.html), but the story that Shawn10538 relates is not representative of them.
Son of God?
This title is not used of Prometheus and is essentially meaningless in a polytheistic theogony. The leading deity in the narratives, Zeus, is not analogous to a Christian "God". But even if he is, Prometheus was not described as his son. Technically, Prometheus would be a cousin of Zeus in Hesiod and an uncle of Zeus (as the son of Ouranos and Gaia/Themis) in Aeschylus.
Born of a virgin?
Not according to Hesiod. He is the son of Iapetus and Clymene, daughter of Oceanus. Iapetus "went up with her into one bed and she bare him ... clever Prometheus, full of various wiles" (Theogony, 507ff; cf. Fabulae, 142, Works and Days, 54). Most other sources similarly posit Iapetus as the father of Prometheus (cf. Quintus Smyrnaeus 10.190, Diodorus Siculus 5.67.1, Apollodorus, Bibliotheca 1.8, Ovid, Metamorphoses 1.82, Valerius Flaccus 4.60, etc.). Aeschylus has a variant tradition, making Themis the mother of Prometheus and identifying Themis with Gaia (Prometheus Bound, 18, 211); the conflation of Themis with Gaia is a later development in tradition, as originally Themis was the daughter of Gaia. This makes Prometheus' father Ouranos, who begat the Titans with Gaia/Khthon (Prometheus Bound, 207). None of these sources portray the birth of Prometheus as a "virgin birth".
Saved mankind by revealing fire to them?
This is a loose but partially valid parallel, inasmuch as Jesus is also a revealer of truth, God, and life in the gospels. It may be a bit of an overstatement to say that Prometheus "saved" mankind; he helped them by giving them the means to cook food and offer sacrifices to Zeus, but he was hardly the only one to help mankind in this way, as he was helped by Hephaistos and Athena who taught the arts and Demeter and Dionysius taught agriculture to people (cf. Plato, Politicus 269a-274d). Aeschylus' version forms a much better parallel, as he attributes to Prometheus all the many functions of Hephaistos, Demeter, and the other gods, by making Prometheus a teacher of culture to humankind (Prometheus Bound, 441ff). But even here there is only the topos of a divine revealer of culture, a near-universal meme in ANE religion (e.g. the apkallu, Shamash, Thoth, Kothar-wa-Hasis in Canaanite myth, the fallen angels in 1 Enoch, etc.), so this similarity is not distinctive or indicative of a special relationship. The specific details and narrative features are otherwise dissimilar. Prometheus steals fire to the displeasure of Zeus in the Greek myth, whereas the theme of theft plays no role in the Jesus story. The version of the myth in Hesiod situates the theft in a longer story about Prometheus tricking Zeus about the kinds of sacrifices humans would offer to him (Theogony, 545-557). Zeus hid fire from man in retribution of Prometheus' ruse, which would have allowed humans to keep the meat to themselves while sacrificing bones and fat (i.e. fire being necessary for sacrifice). Jesus does not appear as a trickster god in the gospels although there may plausibly be a (vague) relationship with the gnostic concept of Christ humiliating the archons. Nowhere does Jesus appear in Christian tradition as deceiving God by faking sacrifices, revealing to man what he has stolen from God (or stolen from the Devil, if the Devil is the appropriate adversary figure), etc. The similarity exists in the very broad outlines, not in details or sub-themes of the story.
Died crucified?
This is a clear exaggeration of the actual Prometheus story, which nowhere construed Prometheus as dying from his punishment; indeed his immortality is pivotal to this part of the story. According to Hesiod, Zeus chained Prometheus to rocks and forced a shaft through his abdomen, exposing his guts to an eagle who would daily devour his liver (which would regenerate in the evening), leaving Prometheus in a perpetual, eternal state of torment (Theogony, 511ff). Aside from the very general topoi of punishment and torture (followed by redemption), the particulars are altogether different. Jesus' torment at the Romans was not eternal, nor was the mode (chaining to rocks, disembowlment, being eaten alive) at all similar. The description of Prometheus' punishment in Aeschylus is substantially similar (Prometheus Bound, 1-122, 907ff). The motif of crucifixion rather appears in the later second century AD satire of Lucian, who used the word stauros to describe Prometheus' configuration. He wasn't literally crucified, he was still affixed to rocks in the story, but instead of being chained, he was described as nailed to the rocks directly in a position that resembles one that is crucified. If that counts as crucifixion, then we have a partial parallel in a post-Christian source (cf. Lucian's Peregrinus on the crucifixion of Jesus the "sage"). It is also worth noting that the punishment of Prometheus in Hesiod and later sources was matched by the punishment of mankind by Zeus' creation of Pandora, the first woman, who unleashed evil on the human race -- a feature of the story that has no analogue in the Jesus story as well.
Resurrected?
Of course, in no sense was Prometheus resurrected since he never died. Aeschylus' lost play Prometheus Unbound, in the fragments we possess, followed the plot provided by Hesiod which portrays Heracles as releasing Prometheus from his perpetual state of agony a thousand years later by shooting the eagle with an arrow and releasing Prometheus from his chains (cf. Apollodorus, Bibliotheca 1.45, 2.119-120, Apollonius Rhodius, Argonautica 2.1238ff, Diodorus Siculus 4.15.2, Strabo, Geographica 11.5.5, Pausanias 5.11.6, etc). One may note a much fainter narrative parallel of actions by protagonist | punishment | vindication/release, but this narrative structure is in no sense specific to this story but is very widely attested in the ANE in a wide variety of stories across genres, such as the court intrigue tales of Ahiqar, Daniel, Esther, etc. This narrative plan IS relevant to the Jesus story and some versions of in biblical literature have further similarities (see JD Crossan's The Cross That Spoke for an analysis WRT the passion narrative), but the specific features of the Prometheus story do not recommend a special relationship with this story (e.g. Jesus was not resurrected by killing/slaughtering/ending what was keeping him in a perpetual state of agony, etc.). And the narrative frame is so general that it structures real-life narratives in which an (innocent) person has been tortured/imprisoned and then later released or vindicated.
The real similarity of the Prometheus story with Jesus is the narrative sequence of (1) individual from higher plane (gods) teaching man (cf. Aeschylus), (2) the same individual gets punished and tortured (+ crucified, at least metaphorically in Lucian's version of the story), (3) this individual is then released from this state. I think it is worth pointing this out, as there is a partial similarity here, and is best only when you pick the certain features of Aeschylus' and Lucian's stories. The parallels with the version in Hesiod are even more general. Parallels are much more impressive usually with OT models, which often supply more narrative elements, motifs, and verbatim phraseology. That is why most studies of the passion narrative focus on parallels with the OT than much more tenuous pagan analogues. That doesn't mean other analogues aren't relevant, but the relevance isn't always due to one being the origin or cause of the other (correlation is not always causation but can also reflect a common millieu).
My main point however is that what is described as "identical" to the Christ story really isn't identical. The Prometheus story rather has been goosied up to better match the familiar narrative of Jesus. Prometheus is described as born through a virgin birth, when the actual sources do not suggest this. He is described as the "Son of God" which has nothing to do with how Prometheus is referred to in ancient sources. He is described as dying crucified when in fact his punishment did NOT involve death and didn't involve crucifixion in early sources (Lucian may indeed be valid but this is uncertain). He is described as resurrected when in fact he was really depicted as liberated from bondage (and perpetual torture). The language chosen in the description of the "plot" of the Prometheus story systematically assimilates it to that of the Christ story, making the similarities closer than they really are. THAT is the kind of thing I am complaining about. Nor is it true that there would be no story left after excising the purported Christ parallels. There would still be the whole story of Prometheus tricking Zeus by disguising sacrifices, or Prometheus getting his liver eaten by an eagle, or Prometheus warning his brother against accepting Pandora as a present from Zeus, or Prometheus assisting the birth of Athena out of Zeus' head, etc.