A rather tight and decent (and potentially pastoral) explanation from Gregory Koukl, an apologist at Stand to Reason:
What makes you think that taking away evil in the world has anything to do with God's strength or goodness?
God certainly is strong enough to obliterate evil from the earth or to have prevented it in the first place. No question about that. But let me ask you a question. Is it a "good" thing that God created human beings as free moral creatures, capable of making moral choices? It strikes me that the answer to that is yes. Because God is good--which is one of the things in question here--God created free moral creatures.
But this changes everything, doesn't it? What makes you think that strength has anything to do with God creating a world in which there are genuinely free moral creatures and no possibility of doing wrong?
You see, now we're back to square circles. It's just as ridiculous to ask God to create a world in which we have genuinely free creatures with no possibility to do wrong, as it is to ask Him to create a square circle. The task has nothing to do with His strength. It has to do with the nature of the problem. If you're going to have morally free creatures--that is, human beings that can make moral choices for themselves--and if God is good, then He is going to create creatures that will be truly morally free. But that entails, of necessity, at least the possibility of evil in the world.
In the Christian point of view, God did the ultimately good thing by creating morally free creatures that went bad...
Read the rest here.
Kudos to JTron for bringing up the excellent question about the suffering which occurs entirely apart from social sinning, such as natural disasters and disease; and kudos to Fr. WB for providing a very good framework for answering that problem in terms of "a broken world." Jill Briscoe, noted Anglican apologist, agrees: in the face of tsunamis and hurricanes, we see the reality of the world which groans until the revelation and redemption of God is final (Romans 8 is right on point here).
I would submit also that people tend to become uncomfortable with these explanations of pain as resulting from a broken world and moral failure; such an answer seems incomplete. In fact, such an answer is incomplete, until both you and your audience have acknowledged your own "breaking" role in the broken world. May I suggest that such a conversation about the problem of pain is a good opportunity to recognize (gently) the sin and brokenness of the one who brings these troubling questions about the reality of pain, and the consequent need for the Savior?