There are two basic versions of the problem of evil: deductive and probalistic (aka inductive). The propontent of the deductive problem of evil attempts to show that the existence of Deductive looks like this:
1. If a God exists who is omnipotent (all powerful) and omnibenevolent (all loving),
2. and evil exists,
3. then God cannot be omnipotent or omnibenevolent.
This version of the argument has been almost completely abandoned by professional philosophers today. It lives on in its popular level form and is made immortal by producing this corpse of an argument between non-philosopher friends. Alvin Plantinga (a preeminent Christian philosopher at Notre Dame and past president of the Amer. Philosophical Assoc., which is the main association of professional philosophers) showed that this version of the problem of evil is logically untenable.
Alvin Plantinga presented a "defense" as opposed to a theodicy. A theodicy is an effort to explain why God would allow evil to exist. A defense, however, merely seeks to show that the atheist has failed to carry their case that evil is incompatible with God's existence. In other words, a sucessful defense with show that the atheist has failed to show that evil is logically incompatible with God's existence, while leaving us in the dark as to why God allows evil.
The deductive argument was destroyed because, in short, the atheist has assumed an overwhelming burden. Premises (1) and (2), above, are at not explicitly, logically inconsistent. An explicit, logically inconsistent statement would be that "God is blue, but God is not blue."
If the atheist thinks that premises (1) and (2) are implicitly inconsistent, then he or she must be assuming some hidden premise(s) that would make the inconsistency explicit. Those premises seem to be these:
(3) If God is omnipotent, then God can create any world that God desires.
(4) If God is omnibenevolent, then God prefers a world without evil over a world with evil.
Hidden premise (3) then is the view that if God is omnipotent, he could create a world that were all humans freely choose to do the right thing. This world would then be free of all moral evil: no lying, no cheating, no murder etc. So, because we can conceive of a world in which everyone freely chooses every time to do the right thing, and God is all-powerful, then God must be able to create it.
This links with hidden premise (4) because if God was powerful enough to create this type of world, then he certaintly would because he is all-loving. In other words, if God had the choice between creating a flawed, evil world like this one and creating one w/o any evil, then God would most certainly chose the latter. Otherwise, God would be evil to prefer that people experience pain and suffering when God could have given them happiness and prosperity.
In David Hume's Dialogues Concerning Natural Religion, he summarized this last point when he asked: "Is he willing to prevent evil, but not able? then he is impotent. Is he able, but not willing? then he is malevolent. Is he both able and willing? whence then is evil?"
Plantinga and others object to hidden premise (3) with what he calls the free will defense. It goes like this: if it is possible that humans have complete freedom to make choices, then (3) and (4) are not necessarily true. If humans have freedom to make choices, then it is not necessarily true that God could have created another world in which no evil exists but people have complete freedom of choice. This is because God's omnipotence doesn't imply that God can do logical impossibilities like create a round triangle or make a married bachelor, or make someone freely chose to do something.
All God can really do is create a world in which a person may freely chose to act and then allow that person to make the free choice. This implies that there are possible worlds that are not feasible for God to create. Just like its not "feasible" for God to create a round triangle or a married bachelor. This does not impinge on God's omnipotence though, because God cannot be impinged for not being able to do a logical impossibility. Another example how how non-sensical this is, is for someone to say that God is not all-powerful because he cannot exist and non exist at the same time.
So, suppose that in every feasible world that God could create, free creatures sometimes choice evil. Here it is us, the creature, not God that is responsible for evil and God can do nothing to prevent their ability to choose the evil, apart from refusing to create such a world at all. Therefore it is at least possible that feasible world that God could create that contains free human beings is a world that has evil in it.
I'm about to say something that will seem crazy and you might be tempted to label be a total fundamentalist and crazy, but please keep reading past the next few sentences. As for natural evils (i.e. earthquakes, tornadoes, etc.) it is possible that these evils could result from demonic activity. Demons could have freedom just like humans and it is possible that God could not preclude natural evil w/o removing demons' free will. You might be thinking, "That is ridiculous!" and you might even think that it is a spurious, frivolous argument. But only let this thought last a few moments lest you confuse the deductive argument with the probabilistic arguments. I admit, ascribing all evil to demonic beings is improbable, but that is completely irrevelant to the deductive version of this argument. Probability only enters the calculus in the probalistic argument. All I must do here is show that such an explanation (both for the moral evil and natural evil) is merely possible.
In summary, hidden premise (3), that an omnipotent God can create any world he desires, is plainly not necessarily true. Therefore, the atheist's argument on this ground alone fails, which causes the whole argument to fail. But we can go further, what about hidden premise (4).
What about (4), the hidden premise that if God is all-loving then he would prefer a world w/o evil over a world with evil. Again, this is not necessarily true. By analogy, we allow pain and suffering to exist in a person's life to bring about some greater good. Every parent knows this. There comes a time when parents cannot protect their child from every mishap, or when the parent must discipline the child so the child matures. Similarly, God could permit suffering in our lives to build us or test us or others and to achieve some greater good. Therefore, premise (4) is also not necessarily true. And again the argument fails, this time on totally separate grounds. Notice that the atheist must show that both (3) and (4) are true, while the theist merely need show one is false.
If I may be permitted to read some of your minds, at this point you might be thinking, "Even if there is no inconsistency between God and evil, surely the existence of God is incompatible with the amount and kinds of evils that actually exist." What good, you might ask, could possibly come from a pregnant mother in the wrong part of town that is struck down by a stray bullet fired from a gang member's 9mm?
This as its own hidden premise, that God cannot have morally sufficient reasons to allow the amount and kinds of evil that exist. But again, this is not necessarily true, and all I must show is that it is possible that God has a morally sufficient reason. As terrible as some things about the world are, people generally agree that life is worth living, from which we could surmise that there is much more good that evil in the world, regardless of the amount and kind of evil actually present. As for the kinds of evil, it is possible that God has some overriding reasons to permit the kinds of evil that occur.
Again, you might think that that seems pretty unlikely. But this would confuse the deductive problem with the probabilistic problem again. To refute the deductive version, the theist doesn't have to suggest a likely solution--all he or she must do is suggest a possible solution.
In summary, the atheist assumes at least two hidden premises in the deductive version of this argument. He or she must prove both of those premises for this version to be true. I have shown that both of those hidden premises can be indenpendently refuted.
Further, because it is the atheist who claims to note a contradicition w/in the theist's truth claims, it is the atheist that bears the burden of proof to show that there is no possible world in which premises (1) and (2) are true. That is an incredibly heavy burden, which the atheist ultimately cannot shoulder. The deductive version of the problem of evil is impotent.
Probabilistic Version
After the deductive argument was destroyed, most who want to use the problem of evil (POE) to show that God cannot be all loving or all powerful moved to the probabilistic argument. The inductive version admits that it is possible for the traditional God of Christianity and evil to coexist, but it is highly improbable for them to coexist. The argument looks like this:
1. If a god exists who is all loving and all powerful,
2. yet evil exists,
3. then it is highly improbable or unlikely that a god exists who is all loving or all powerful.
Let me make a few observations. Notice that even if the Christian granted this argument, this argument does not show that God does not exist. It is, however, a step along that path. At most, this argument can claim that the type of God posited by traditional Christianity does not exist. Further, this argument cannot show that God is not all loving and not all powerful; it can only show that one of this is incorrect. But this is all only the case if we grant this argument, and there are powerful reasons not to grant it.[/u]
Given that this post is way too long already, I'll be brief here, and will flesh out my comments on this version as other posts come in (if anybody actually gets this far into the novel
(1) Given the full scope of the evidence for God's existence, it is far more likely than not that God exists.
(2) Because of our finite nature, we are not in a good position to asses with a sufficient confidence that God has no morally sufficient reasons for permitting the evils that occur.
(3) Christianity entails doctrines that increase the probability that God and evil coexist
I look forward to your comments.
You see, "fully free-willed and fully incapable of sin" is exactly what the theists would have us believe the situation to be in heaven when we go there after death. We can only assume that when we enter heaven, we are made incapable of sin 
(there can be no sin in heaven, of course) but somehow God is able to retain our free-will - after all, if God doesn't want pre-programmed robots on earth, then he certainly doesn't want them in heaven! And we wouldn't want it either - take away our free will, and it's not "us" up there, it's some lobotomized version of us that we wouldn't even recognize. 
