Throughout history, one of the biggest questions asked about God, by both believers and unbelievers alike, is "if God is so good, why does He allow evil"? Even as far back as the 7th century B.C., Habakkuk says that God is so pure, He can't even look at evil, and so he asks how is He able to tolerate the wicked?
The answer is in the question. God is too pure to look at any evil. When we, as sinners, think of evil, we tend to categorise it. We have a high category, in which we typically place murder, rape, paedophilia etc., then we have lower categories like theft, and then we have things that we don't even think are that bad, like fornication or gluttony. But God doesn't have the same mindset. Not that all sin is equal, as some mistakenly say, but as all sin is against Him, to offend even once makes one guilty of all (James 2:10). As a broken mug is a broken mug, a broken law is a broken law. What that means is that God can't look at someone as evil as Stalin, but He also can't look at someone as evil as... Habakkuk. Habakkuk, even as a prophet, was a filthy sinner, worthy of God's wrath, and but for God's grace, destined to receive it.
There are, therefore, two important aspects to God that must be considered when answering the question of evil: His justice, and His love. God's justice means that all sin must be punished, whether great or small. But God's love means that He really doesn't want to. He wants to forget our sins, and not only show us mercy, but bless us exceedingly. He wants that so much that He made the ultimate sacrifice at the cross. Rather than finite beings like us taking an eternal punishment, the eternal being of Jesus took a finite punishment on our behalf. That allows God to completely forget our sins, His wrath against sin completely satisfied forever.
But that gift only applies to those who dare to tear open the wrapping paper. If you leave it in the box, it doesn't count. If you die without opening that box, you face the eternal punishment God owes you for your sins. So what's the solution there? God waits. God gives a grace period. This obviously varies from person to person. Some people die at a ripe old age, others are killed before they're even born (though of course, having no sins to speak of, they are saved). But during that grace period, sinners can continue sinning. God can kill an evil person in the process of sin, but if He spares such a person, they can repent later.
Take Jeffrey Dahmer, for example. Dahmer was a mass murderer. God could have killed him as soon as he'd intended to kill his first victim, at which point Dahmer, then an Evolutionist, would have been sentenced to an eternity in Hell. But in sparing Dahmer's life, God gave him the time to repent, which eventually he did. This not only spared Dahmer, who will now spend eternity with a restored relationship with God, but his testimony may also be a stepping stone in someone else's walk with God. Maybe, and I pray that this will be so, someone might even read Dahmer's example and themselves be saved.
There are so many factors that must be taken into account that we will never truly know exactly why God permits specific evils. What can be guaranteed, however, is that God doesn't want a single human being in Hell (2 Peter 3:9). If you're a Christian reading this, remember next time you wonder why God lets bad things happen, be grateful that He allowed the worst possible thing to happen (the crucifixion of Jesus) to atone for your own evil. If you're not a Christian and you're reading this, next time you ask why God lets bad things happen, remember that if He was to bring judgement upon you now, you will spend eternity in Hell, separate from Him. He doesn't want that. You don't want that. I don't want that either, so I'm going to encourage you to make good use of your grace period. Repent of your sin and turn to God. A time will come when evil will perish, and no more bad things can happen. Ensure you enjoy the Kingdom His blood bought for you.