Inherent Evil

[Lord of Angmar]

The stain of Melkor was innately put upon everything in Arda's beginning; Orcs may have been unremovably there because of this.

Good point Gwaihir. Although I do not think this really qualifies as an explanation of orkish existence, it is a good reason to believe that orcs can be redeemed. Since Melkor put forth much of his power into Arda itself, and since his power was reflected in Ea through his rebellion in the Themes even before Ea was created with the Flame Impherishable, then his evil was inherently part of the landscape. Since orcs are a product of the marring of Iluvatar's world, then I would think that they would be purged in the afterlife (since the halls of Iluvatar and the Undying Lands remain unmarred, and that is where they would probably be judged) and follow the fates of their ancient kin (whether they are Men, Elves, Maiar or beast).

Now to punishment, which I think everyone here has touched upon except me. I believe that for orcs, the punishment (if any) put forth by Iluvatar or the Valar before absolution would more closely resemble purgatory than hell. In fact, I do not think that there is an equivalent of hell in Tolkien's world, unless it be the dungeons and fortresses of the Dark Lord (Angband, Utumno, Mordor, etc.) I think once they were absolved of their sins (whether this would involve a long wait and/or punishment respective to their crimes I do not know), I believe, as I said earlier, that they would follow the fates of their original ancestors.