Why does [a good] God let bad things happen?
Why wouldn’t he?
God is Love (meaning that it is one of his strongest characteristics.)
There can be no true love without free choice. God could take away all options for sin, remove the disease, the death, the torture, the abuse, and the hatred, because be assured… he IS GOD. But He doesn’t. For there to be Love, there must be choice. A person who is forced to Love is a slave, not a free being. If there is wrong choice, there are bad consequences. To have it any other way, wrong choices could never be corrected. To take away the consequence of sin is therefore to remove the mechanism that is designed to bring us back in line with our intended purpose: fellowship (love) with God.
Since God is Love, Anti-God (Satan) is hatred. Hatred has it’s own set of rewards. There are benefits to being selfish. Ask any alcoholic–it’s called a high. Ask any child or spouse abuser, it’s called a sensation of power. Ask any liar or cheat, it’s called dishonest gain, otherwise known as wealth. Unfortunately, the side-effects of hatred are disease, self-hate, emotional destruction of the victims of your actions, etc. Hence, the “bad things”.
So why do bad things happen to innocent or good people? Because we are not alone. Our lives intersect in some sort of cosmic or spiritual three-dimensional-web-thingie, where our actions affect other lives. A random sickness or death over here, makes people over there think, pray, change. Our stories are not our own, and people truly can and do affect the lives of others, for better or for worse.
See the Sovereignty post in Jesus.