Back in the comments section of my post on Giving Thanks, an old college friend and I are discussing the age-old problem of why God permits suffering and other evils. This is a serious problem; in my view the Argument from Evil is the only really formidable positive argument for Atheism. (By a positive argument for Atheism, I mean something that provides specific evidence against God's existence, rather than merely making the negative claim that there isn't enough evidence for Theism to believe it. In order to show that Christianity is plausible, both claims must be addressed.)
The conundrum is famous: If God is the All-Knowing, then he knows what things are evil, if he is the All-Powerful, he should be able to prevent them, and if he is the All-Loving, then he will want to prevent evil. So why is there evil?
The only way to solve the problem is to postulate the existence of some good thing which cannot exist unless evil either exists, or is at least possible. (Common "defences" might refer to putative goods such as free will, the opportunity for humans to exercise virtues, the orderliness of the universe, an afterlife of a sort that depends on people having had certain experiences, etc.) If the good is such that it is logically impossible to get it without (possibly) getting the evil too, then the defence would be successful, since when we say that God can do anything, we don't mean that he can or would create a logical contradiction. (As C.S. Lewis says in The Problem of Pain, "Nonsense remains nonsense even when we talk it about God.") I'm not going to attempt a detailed defence here, but I do want to make some general points about the Argument from Evil.
My first point is that God's omniscience actually makes the Argument from Evil weaker, not stronger. The reason is that we humans are not omniscient. If we are ignorant, there's no particular reason to assume that we know what is the morally best way to run a world. Suppose that you wrote down a list of all the things you regard as good (happiness, knowledge, beauty, whatever). Suppose you figured out a way to weight all of these factors numerically—of course, there's no way we could ever agree on how to do this, and I'm not convinced it even makes sense, but let's run with it—so that you could assert that some possible kind of universe (call it ) is optimum: the best possible.
[Note for experts: my kinds of universes here aren't exactly the same as the "possible worlds" discussed by analytic philosophers. If the best possible kind of universe contains something like free will or nondeterminism, there will be multiple "possible worlds" consistent with the same overall plan of the universe, some of which may be morally better or worse compared to the others.]
Now if God knows about even a single kind of goodness that we are ignorant of, or if he weights the various kinds of goodness differently than us in any way, then of course God will view some other kind of universe as best. It seems infinitely unlikely that just by coincidence, so it seems to be almost certain that the universe will appear to us to contain evils that we can't explain. One can argue about whether this is a sufficient explanation, but it's definitely something that has to be taken into account. The idea that a superhuman entity which created the universe will see things exactly the way we do is absurd:
“For my thoughts are not your thoughts,
neither are your ways my ways,”
declares the Lord.
“As the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.”
The second point I'd like to make, is that the Argument from Evil has emotional force as well as intellectual force. Atheists tend to get annoyed when Theists suggest that Atheists don't believe in God because they resent him. I've certainly seen plausible cases of this, but I don't want to speculate that all Atheists are this way, since I don't like making unfounded accusations about individual people's characters. (Maybe that's why my Politics category only has one post in it so far.)
Nevertheless, leaving the Atheists aside for a moment, I think I can say from an examination of my own heart, and conversations with other people, that it's easy to carry an unconscious grudge against God for various real or imagined grievances in our lives, or the lives of those we care about. Even if we have no grudge, there can be a deep sense of pain from all the kinds of grief that we don't understand.
So the Argument from Evil carries emotional force as well as intellectual force. There's no necessary reason why an intellectually satisfying answer should be an emotionally satisfying answer, or vice versa. One should bear this in mind when evaluating the intellectual arguments, since we may be asking from an argument something that no argument can do.
Finally, I believe that Christianity has resources for addressing the Argument from Evil which don't exist in generic-brand Theism, or indeed in any other religion. It's much too simple to say that the existence of evil contradicts Christianity, when in fact the most basic doctrine of Christianity logically implies the existence of evil.
The basic doctrine is that 1) we human beings are wicked and deserve punishment, and that 2) in order to forgive us, God became an innocent human being and allowed himself to be tortured to death by us, and that 3) this act provides us with spiritual healing now, as well as physical immortality for all eternity. Now regardless of whether you like this idea, even if you find it implausible or downright incomprehensible, you must admit that it's an idea about how God relates to evil, and uses it for the sake of good. If there were no such thing as innocent suffering, Christianity wouldn't even be possible. If Christianity is true, then God has arranged things so that the most important thing that ever happened was a horrible but redemptive evil. All other evils, we view in the light of the Cross.