This is an issue where BaptistBoard has been helpful to me. About a year ago this topic came up, and I posted some tentative thoughts about hell literally being destruction, hoping that if I was wrong, I'd hear good biblical reasons in the thread. Instead, the thread ended up confirming what I posted, only dealing with arguments I had already mentioned. Anyway, here's what I posted then, and what I still think now:
One of the main reasons I'm uncomfortable with the literal eternal flames view is that it appears to be based on taking literary passages literally while reinterpreting the clearer passages. For instance, Revelation 14:10-11 and 20:10-15 describe torment in the lake of fire, but what is interesting is who all is being tormented. Revelation 20:14 says, "Then Death and Hades were thrown into the lake of fire. This is the second death, the lake of fire." To me, this seems to not be literal, since I don't see how something like death can be tormented by fire. We know from other passages that death will be conquered and be no more. This passage seems to be a picture of that rather than a concrete, literal reality.
The other main prooftext is the story of the rich man and Lazarus, and personally I think there's strong reasons for considering that story to be a parable. It may even be a Jewish story that was already commonly known that Jesus turned on its ear by giving it a new twist. In any case, I don't think a doctrine on hell should be formulated mainly from a symbolic vision and a possible parable.
The more prosaic descriptions of the destiny of the wicked often seem to point to eventual destruction. John 3:16 presents two options: to gain everlasting life or to perish. While I do think the wicked will be raised to face judgement, I don't think they will also be given everlasting life to spend in a different location. Matthew 10:28 says, "And do not fear those who kill the body but cannot kill the soul. Rather fear him who can destroy both soul and body in hell." Other similar verses include 1 Corinthians 1:18, 2 Peter 2:12, and 2 Peter 3:9.
There's also interesting examples used of what the eternal punishment is like. Jude 1:7 says that the destruction of Sodom and Gomorrah serves as an example of the punishment of eternal fire. The only way to add eternal torment to that is to say that the residents of Sodom and Gomorrah are now being tormented eternally by fire. But, that requires reading a presumption of eternal torment into the text regardless of what it states, and it also negates the historical example of what happened to the cities, which is what Jude refers to. Mark 9:43-48 speaks of a place where flames and worms are eternal, but it does not say that those thrown into this place will live forever. In fact, by checking the passage Jesus quotes in Isaiah 66:24, we see that it is talking about dead bodies being consumed by worm and flame in a garbage dump, and not about torment of living souls.
This view also allows a more literal interpretation of the passages that talk about hell being more bearable for some, and of some being beaten with more blows than others. There may be a form of torment (varying from person to person), but the end of it is destruction. To me, that seems more likely that a Dante-esque hell broken into sections with different settings on the thermostat.
Finally, this view seems consistent with the idea that hell is separation from God. According to 2 Thessalonians 1:9: "They will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might..." While people can be separated from God today, ultimate separation must result in ceasing to exist, because God is the eternal I AM. Because God is and God is omnipresent, to be totally separated from God is to not be. Because of this, that wonderful prophecy from 1 Corinthians 15:28 can some day be fulfilled: "When all things are subjected to him, then the Son himself will also be subjected to him who put all things in subjection under him, that God may be all in all." God may be all in all because in eternity nothing will exist that is in rebellion to God.
About the only verse that gives me second thoughts about the eventual destruction of the wicked is Matthew 25:26: "Then they will go away to eternal punishment, but the righteous to eternal life." But even here, destruction is a punishment with eternal consequences: due to this punishment, the wicked will not exist for all of eternity.