The Bible describes God as holy (Isaiah 6:3), righteous (Psalm 7:11), just (Deuteronomy 32:4), and sovereign (Daniel 4:17-25). These attributes tell us the following about God: (1) God is capable of preventing evil, and (2) God desires to rid the universe of evil. So, if both of these are true, why does God allow evil? If God has the power to prevent evil, and desires to prevent evil, why does He not prevent evil? Perhaps a good way to look at this issue would be to consider some alternative situations for how people might have God run the world:
1) God could change everyone’s personality so that they cannot sin. This would also mean that we would not have a free will. We would not be able to choose right or wrong because we would be “programmed” to only do right. Had God chosen to do this, there would be no meaningful relationships between Him and His creation.
Instead, God made Adam and Eve innocent but with the ability to choose good or evil. In doing so, they could respond to His love and trust Him or choose to do their own thing. They chose to do their own thing. Because we live in a real world where we can choose our actions but not their consequences, their sin affected those who came after them (us). Similarly, our decisions to sin have an impact on us, and those around us.
2) Another choice would have God compensating for people’s evil actions through supernatural intervention 100% of the time. For instance, if a drunk driver causes an automobile accident, God would have to keep him and the people in the other automobile from getting harmed, for there would be many people who could possibly be caused to suffer from the accident or the death / injury of those involved in the accident. God would have to keep the drunk driver from crashing into power lines, buildings, etc. because these things would cause innocent people to suffer.
Another instance might involve a lazy person plumbing a house, and he doesn’t bother to check the plumbing for leaks before the house is finished. God would have to make the plumbing not leak because otherwise the home buyers would have to suffer for the lazy person’s sin.
If a father gets addicted to drugs and spends all of his money on drugs, God would somehow have to miraculously provide both the food and the social needs of the children so that they would not have to be adversely affected by the evil of the parent.
In such a world, God would be like a bad parent who enables a wayward child’s destructive behavior. There would be no consequences for one’s actions, and as a result no one would learn integrity, purity, honor, responsibility, or self-control. There would be no “good consequences” for right behavior, no “bad consequences” for wrong behavior. What would people become except more deviant and sinful?
3) Another choice would be for God to judge and remove those who choose to commit evil acts. The problem with this possibility is that there would be no one left, for God would have to remove us all. We all sin and commit evil acts (Romans 3:23; Ecclesiastes 7:20; 1 John 1:8). While some people are more evil than others, where would God draw the line? Ultimately, all evil causes harm to others.
Instead of these or other options, God has chosen to create a “real” world in which real choices have real consequences. In this real world of ours, our actions affect others. Because of Adam’s choice to sin, the world now lives under the curse, and we are all born with a sin nature (Romans 5:12). There will one day come a time when God will judge the sin in this world and make all things new, but He is purposely “delaying” in order to allow more time for people to repent so that He will not need to judge them (2 Peter 3:9). Until then He IS concerned about evil. When He created the Old Testament Laws, He established laws that discourage and punish evil. He judged nations and kings who disregard justice and pursue evil. Likewise in the New Testament, God states that it is the government’s responsibility to provide justice in order to protect the innocent from evil (Romans 13). He also promises severe consequences for those who commit evil acts, especially on the "innocent" (Mark 9:36-42).
In summary, we live in a real world where our good and evil actions have direct consequences and indirect consequences upon us and those around us. God’s desire is that for all of our sakes we would obey Him that it might be well with us (Deuteronomy 5:29). Instead, what happens is that we choose our own way and then we blame God for not doing anything about it. Such is the heart of sinful man. But Jesus came to change men’s hearts through the power of the Holy Spirit. So He is able to do for those who will turn from evil and call on Jesus to save them from their sin and its consequences (2 Corinthians 5:17). God does prevent and restrain some acts of evil. This world would be MUCH WORSE were not God restraining evil. At the same time, God has given us the ability to choose good and evil, and when we choose evil, He allows us, and those around us, to suffer the consequences of evil. Rather than blaming God and questioning God for why He does not prevent all evil - we should be about the business of proclaiming the cure for evil and its consequences - Jesus Christ!
http://www.gotquestions.org/God-allow-evil.html