Why does an all-loving, all-powerful God allow suffering in the world? Moral suffering is suffering that we caused or could have prevented based on choices we made. We can't blame God for this sort of suffering because we made choices out of our own free will that caused suffering. We couldn't have freedom or love if we didn't have free will.
What about suffering that comes from things that we didn't cause or couldn't prevent? The following parable might help illustrate this complex question.
Once upon a time, God created a whole bunch of people and sat them down in front of a huge banquet table filled with every sumptuous food imaginable. They were very hungry and tried to eat, but God had seemingly neglected to give them elbows. Every time they tried to get the food to their mouths, their hands were too far away. People were beginning to die of starvation while seated before a sumptuous feast.
A group of people seated at one end of the table speculated, "God must be very stupid, or He is not all-powerful. Because if God were smart, He would have known that we need elbows to eat; and if He were powerful, He would have been able to make them." Depressed at the thought of being stuck with a God who could not help them, they turned to the second group of people for advice.
The second group answered, "Look around at the trees, the oceans, and the sun. God must certainly be all-knowing to have thought up all of this. And he must be all-powerful to create it all. The truth must be that God is mean and selfish and filled with anger and revenge. And that is why we have to suffer." At the thought of being stuck with a horrible God, these people became very afraid, and in imitation of their "angry God," they began to turn on one another in violence.
Another group of people cried out: "Stop! You just admitted that God must be all-powerful. But what is the most positive power that exists in the world? Of course, it is love. So if God exists, He must be all-powerful. And if He is all-powerful, He must be all-loving. Therefore, because we are suffering, God must not exist." At the thought of a world without any God at all, the people around the table became very cynical. And they sat in protest until they began to starve to death.
Finally, the fourth group were watching all of the activity around the table. And as they were watching, they caught a glimpse of the eyes of the suffering people who were sitting across from them. And they noticed a goodness in the eyes of the other. They saw intrinsic dignity and someone of great worth sitting before them. They were incited by compassion to use their elbowless arms to feed the person across the table from them. They discovered how to feed and be fed in an act of compassionate love. And it was in this selfless act of goodness that the people with no elbows discovered the true meaning behind their suffering...love.
If God's purpose is the teach us how to love, then it is likely that the purpose of all suffering arising from natural causes is precisely to teach us to love. If we are looking for love in our suffering and trusting God, love will arise out of our suffering both for ourselves and for other people. Agape (love) is stronger than the culture of death.