There are two issues in the problem of evil. First, why does evil exist? Second, why does God not do anything about evil? I have no answer to the first, but I can answer the second in a way I am sure has never been used. A solution lies in David Lewis's conception of possible worlds (all of the ersatz versions of Lewis's views will not work, offering perhaps another reason for some to accept Lewis' views.)
Lewis holds that claims like "There are apples," "There are numbers," "There are ways the world might have been," all make existential claims: these things exist. He calls the ways the world might have been "possible worlds" and asserts that they exist exactly like this one. These are not collections of propositions, or ideas in the mind of God, etc., etc.. Each possible world is a universe unto itself, some with people much like you and I, some without. Whenever there is a true sentence like "There might have been no people", it is true because there is a universe (space-time continuum) like this one at which there are no people (it does get more technical, see Lewis Counterfactuals and On the Plurality of Possible Worlds). So, too, for any true claim about what might have been.
Now the idea behind wondering why God does not do anything about evil or suffering is plain enough. If He is all good, he has a moral obligation to end evil and suffering. If he is all powerful, He has the power to end all evil and suffering, and if he is omniscient, he will know how to end all suffering and evil. If he did intervene, he would make this world a better place, reduce suffering and evil.
If Lewis is right, this world is one among an infinite number of worlds. Let us call some evil E, and our world e. The sentence "God could end E" is true at e. That means at some other world, p, God does end E. But here is the deal: for the totality of evil and suffering across possible worlds, there is no change at all. And if he acts here, but might not have, then there is someplace else where he does not act, and hence the evil we avoid here exists on another possible world. Whether God acts or does not act, the total amout of evil and suffering remains the same. Hence, it is not wrong for God to prevent E.
Now if there is no possible world in which E does not exist, then it is impossible for there not to be E. We cannot hold God responsible for not doing the impossible.
Given that He makes a world, if he only makes one, then everything at that possible world is necessary. It is the only possible world. It is then impossible for God to have done otherwise, too. God could not have made another possible world, because the existence of possible worlds is what makes anything possible.
The world exists. It contains evil. Possibilities exist. They can be more or less evil. But it is impossible for the totality of evil to be greater than or less than it is, across possible worlds.
And don't come back with "But that is unbelievable." We are already assuming God's existence. Is that so much easier to believe than Lewis' possible worlds?