We (Oriental Orthodox) don't believe in Purgatory. We believe that all the righteous and unrighteous who lived in the Old Testament went to the gave, Hades when they died. The rightous awaiting the Christ, and the unrightous awaiting the lake of fire. When Christ died on the cross, His Spirit and His Body were separate, as happens to all of us when we die, but both His Spirit and His Body remained united to the Godhead. His Body lay in the Tomb, and did not decay since it was united to the Godhead. His Spirit decended into Hades like all others, but since He had committed no sin, Satan had no power to hold Him. He preached the Gospel in Hades, explaining to the OT figures the role they played in the history of salvation. He then broke assunder the gates of iron and the bars of brass (or however the Psalm goes), opened the way to Heaven, and lead the righteous there as He was Ressurected.
Now when people die (or properly, depart since there is no death for the Christian) they are immediatly judged and go either to Heaven, or to Hades. At the end of time, the bodies will be ressurected, and we will stand at the final judgment, where our deeds will be revealed. The unrighteous will be cast into Hell, the lake of fire, and the rightous will go with Christ to the Heavenly Jerusalem.
Catholics have come up with the idea of Purgatory as a transitory place (or state) between earth and Heaven. They say that we must be purged of all sins by suffering before being ready to enter Heaven. This is adding guilt, the same as adding the penance to confession. No amount of suffering can make us worthy to be with God in Heaven, only Christ's blood can. Even Catholics admit that those alive at the Second Coming will not go to Purgatory, but will be "instantly purgated" and stand at the final judgment. I've never heard an explanation for why Purgatory is not needed here, but is in other places.
We don't pray for the dead because we believe they are suffering before Heaven. We pray for them because we believe that we are not separated, that we are still one community, and we are brought together through prayer. The prayers for the dead are consoling to those still here. Also, God is not bound by time, so just because the person is already judged does not mean that the person does not benifit from them. I for one don't understand how my prayers help people here on earth, and yet I trust that they do. I'm not surprised then that I don't understand how my prayers trust the dead, and yet I trust that they do. It is Biblical, and it has been the practice of Christianity at all times over the past 2000 years.