Why does God allow suffering?

Skeptics often ask this question, suggesting some criticism of God.

I would ask them, "Have you ever allowed suffering, when you could have stopped it?" Most people's honest answer would be, "Yes." I would then ask them, "Why?" It does not matter their reasons. What matters is they recognize there are good reasons to sometimes allow suffering, even when it can be stopped.

For example, a painful medical treatment that keeps one from dying.