Why does God permit evil? Ask most Christians that question, and the answer you will get is "free will." This is also the typical response on sitcoms such as Highway to Heaven and Touched by an Angel.
According to their reasoning, God created humans with the ability to choose. He wants them to follow him and his way out of their own volition, not because they are forced to do so. After all, we're not robots. And most of us would prefer to receive love from someone who chooses to love us, not from a robot who has no choice. The same is true with God, so God has given human beings free will. Yet, by so doing, he took the risk that a lot of people would not follow him and his way. Rather, many would choose to be selfish and hurt one another. The result is the human evil that you see around you.
This is a typical Christian theodicy, though I would hesitate to say that all Christians believe it. Calvinists, after all, maintain that God programs a select group of people with the ability to love him. For them, humans in their natural state are totally depraved, meaning that they cannot choose to love God because they are innately sinful. Technically, Calvinists hold that sinners do their sins voluntarily, so they are responsible for them. But the typical "free will" theodicy does not work overly well within the Calvinist system of beliefs, for they think that God can and does program people to do the right thing (on some level). In a sense, Christians are robots within their ideology, notwithstanding Calvinist denials. And, if God can program people to love him, then why doesn't he do that with everybody? Human evil would then cease, or at least decline significantly.
But a lot of Christians talk as if free will is an absolute value that God never violates. "God can't prevent evil because he gave humans free will," they say. Or, as Monica the angel says on Touched by an Angel, "God's not responsible for your pain. The person who caused it is. Where was God? He was weeping for his children." The episode that was on today used that line of reasoning with respect to the Holocaust.
But, biblically speaking, there are times when God overrides human free will. Or at least he influences (or, more strongly, causes) people to choose a certain path. God hardened Pharaoh's heart (Exodus 4:21; Romans 9:17-23). He also hardened the hearts of the Canaanite kings so that they went out to fight the Israelites rather than surrendering to them (Joshua 11:20). God stirred up the spirit of Cyrus, king of Persia, to allow the Jews to return to their homeland (Ezra 1:1). And Proverbs 21:1 says, "The king's heart is a stream of water in the hand of the LORD; he turns it wherever he will" (NRSV). So God can influence people in a certain direction to accomplish his purposes. And such influence seems to undermine human free will, since God is not exactly leaving people to their own devices in those situations.
So free will is not really a good excuse for the existence of human evil, since God can cause people to do good if he so desires. Sometimes, he does. Often, he doesn't.
In some parts of the Bible, God appears to be intimately involved in day-to-day life. Proverbs 16:9 affirms, "The human mind plans the way, but the LORD directs the steps" (NRSV). And God brought blessings and promotion to Joseph by giving him favor in the eyes of various officials (Genesis 19:21). God also granted the Israelites favor in the eyes of the Egyptians, allowing the Israelites to leave without trouble and with a lot of wealth (Exodus 11:3; 12:36). So God is able to bring blessings to his people by manipulating the will of others. Some say, "God can't make someone like another person." Well, there were times when he did just that.
At other times, however, God just lets nature take its course. Throughout the prophets, God condemns unjust judges who favor the rich over the poor, thereby allowing oppression, exploitation, and suffering to continue. But why didn't God grant those poor victims favor in the eyes of the judges? He was able to do so. Instead, he let the unjust judges give their unjust verdicts. As a result, he permitted unfair suffering to exist. Sure, God was concerned, and he demonstrated his righteous indignation when he brought about the destruction of Judah and Northern Israel. But he tolerated injustice for such a long time. And why didn't he simply correct specific unjust situations, rather than destroying entire nations? In the prophets, God appears to be involved in a big picture sense, not so much on a day-to-day level.
So there are many times when God respects human free will. And there are times when he overrides it to accomplish his righteous purposes. We can't put God in a box on this issue.