Kosta is absolutely right that most Orthodox believe that Mary's body was taken up into heaven (*after* her death and burial.) There is an entire story about St. Thomas not being at her death and burial, and then going to her tomb, only to find it empty, and seeing in a vision that she was assumed into heaven, etc... I personally accept this general story as reflecting the consensus tradition of the Orthodox Church.
What is interesting is that the liturgical services of the Orthodox Church are *very* ambiguous on this point. If you read the texts for the services of the Dormition, I'm not sure that one would come away knowing that we believe in her being taken up into heaven in the body.
I seem to remember writing a lengthy post on this sometime in the distant past, quoting the relevant portions of the services. The emphasis in the services is that she died and that her soul was taken to heaven. There are a couple of oblique references to her body -- if I have time, I'll look them up.
It is perfectly acceptable for an Orthodox Christian not to believe that she was assumed bodily into heaven after her death (as with so many things, we don't dogmatize a whole lot -- and if something isn't clear in what we pray it is probably not a dogma.) I personally believe that she was, but there are people I respect who doubt the veracity of that particular part of the tradition, and their arguments are legitimate.
I don't see how the Orthodox version of this -- namely that Christ did not want his mother's body to suffer corruption and decay, and also wanted to give to the world a foretaste of the resurrection awaiting us ordinary mortal Christians (just as Mary was an ordinary mortal Christian) -- is blasphemous in any way.
Enoch and Elijah were taken up into heaven bodily without death (although we in the Orthodox Church believe that they will return as the two witnesses, and *then* be killed at the end of time.
As to a body being taken up into heaven after death, we have the witness from the Epistle of St. Jude, where the Archangel Michael and Satan are disputing over the body of Moses. Why dispute over his body if not for the reason of taking it up to heaven? Just as no man ever found Moses' body or grave according to the Scriptures, so also no-one has ever identified a grave or any relices of the Theotokos. For someone of her importance to the Church, one would expect that this would not be the case.
The two who appeared to the disciples on Mt. Tabor were Moses and Elijah -- besides the obvious summary of law and prophets, I find it interesting that in both cases, something unusual happened to their bodies. The one was assumed into heaven without dying, and with Moses, I don't know exactly what happened, but between what Deuteronomy says and Jude says, it wasn't the ordinary, run-of-the-mill thing...
Has a "reasonable" positive identification ever been made on any of the grave sites of any of the Apostles? (I don't know.) I'm sure there are plenty who "believe" that so-and-so is buried "here", and churches have probably been built on such beliefs. I'm just wondering if there is a widely accepted consensus in any particular case. To my knowledge, even the tomb of Christ has not been positively identified.