The question implies that if a good God exists, then evil shouldn't because God, being all powerful, should stop it.

We need to ask and answer two questions. First, what is evil? It is that which is against God. It is anything morally bad or wrong. It is injurious, depraved, wicked. Some acceptable examples might be murder, rape, stealing, lying, and cheating. Second, if we want God to stop evil, do we want Him to stop all evil, or just some of it? In other words, if just some of it, then why? If He were to stop only part of the evil, then we would still be asking the question, "Why is there evil in the world?"
     Let's suppose that someone was about to commit murder. God would have to stop him, maybe whisper in his ear, or if that didn't work, do something a little more drastic, like have something fall on him, or stop his heart, or make his hands suddenly fall off. Anyway, God would have to do something.