Why does God allow evil?
So we've covered that evil isn't an actually existing thing, and we've covered that the reason evil is around is due to the free choice of moral agents. But another question presents itself: Why does God give any agents free will in the first place, given that he knows that they will sin?
There are a couple of answers to that. First, God is essentially loving. This means he is not only in a disposition to love (character-wise) but actually loving of all. The reason God created moral agents is because that love relationship can only be reciprocal in the case that the object is also capable of love. But only moral agents are capable of love (because love is an objective moral value). Think of it like a parent: you know that, before conceiving a child, that the child will do things contrary to you, and even break your heart. But that doesn't overcome or outweigh the potential for love. The same basic reasoning applies. God knows precisely what will happen, but he also knows the only way there can be creatures in his image is for them to be moral agents. They must be free in order to be moral agents (a causally determined agent may follow all the rules, but he isn't commended for doing so, anymore than a GI Joe is truly commendable when a child pretends he has destroyed the bad guy's headquarters).
The next answer as to why God allows evil is found in this five-word answer, given to me by Dr. Tim McGrew: God knows something you don't. Given that only free creatures can be loving, moral agents, there are going to be a lot of truths concerning how actions affect, directly and (mostly) indirectly, other events in the world. Since God cannot force someone to freely do something, it's a logical truism that God cannot avoid a world with evil, if free creatures are going to rebel (which, plausibly, any non-divine moral agent, given enough time and opportunity, will rebel against God). But why should that constrain God not to create? Why should the joys of this world be overturned by evil?
Now I would agree that, were there to be no ultimate and final reckoning of evil, that perhaps God should not have created. But God has provided a mechanism for dealing with evil ultimately and finally. That mechanism has as its ontological basis the death, burial, and Resurrection of Jesus Christ. Jesus Christ is the Son of God, sent from Heaven to Earth to live as a man. He lived a sinless life, a life without any evil whatsoever, as only a divine person could do. He was executed on a Roman cross at the behest of some of the Jewish leaders who were not too thrilled about his message. This execution, though unjust by its very nature, was counted by God as a sacrifice for sins; it was the perfect paying for unrighteousness by death on behalf of those who could never do this, even in principle. By raising him from the dead, God validated the message of Jesus (since, plausibly, God would not raise a blaspheming heretic from the dead). On Christian theology, evil finally will be dealt with at the "end of the age," where evil will be eternally abolished and those who have not rejected but accepted Christ will be with him forever.
Now ask: why does evil exist on any other worldview? Every worldview has to deal with the reality of the negation of moral goods. Someone might just say there are no moral values, but then he loses his justification for moral outrage at God for allowing evil. Any view that explains away, rather than explains, evil, we should cast a wary eye toward. Christianity not only accounts for the existence of evil, but its abolishment as well!