This is perhaps the most contemplated and debated question in regard to the existence of God. So instead of offering up my own thoughts on this, I turn to a much greater mind: Tim Keller. The following is an explanation of the issue along with Keller's brief response. For more, see his book The Reason for God.
The Question: Christianity teaches the existence of an all-powerful, all-good and loving God. But how can that belief be reconciled with the horrors that occur daily? If there is a God, he must be either all-powerful but not good enough to want an end to evil and suffering, or he's all-good but not powerful enough to bring an end to evil and suffering. Either way the God of the Bible couldn't exist. For many people, this is not only an intellectual conundrum but also an intensely personal problem. Their own personal lives are marred by tragedy, abuse, and injustice.I would simply add this Scripture for the broken and hurting:
Brief response: If God himself has suffered our suffering isn't senseless. First, if you have a God great and transcendent enough to be mad at because he hasn't stopped evil and suffering in the world, then you have to (at the same moment) have a God great and transcendent enough to have good reasons for allowing it to continue that you can't know (You can't have it both ways). Second, though we don't know the reasons why he allows it to continue, he can't be indifferent or un-caring, because the Christian God (unlike the gods of all the other religions) takes our misery and suffering so seriously that he is willing to get involved with it himself. On the cross, Jesus suffered with us.
Hebrew 4:14-16 (ESV)
Therefore, since we have a great high priest who has gone through the heavens, Jesus the Son of God, let us hold firmly to the faith we profess. For we do not have a high priest who is unable to sympathize with our weaknesses, but we have one who has been tempted in every way, just as we are—yet was without sin. Let us then approach the throne of grace with confidence, so that we may receive mercy and find grace to help us in our time of need.