A question or statement that many people put forward to deny that God exists, often to also try to deny that he's a good God, is the existence of evil. God made evil, if he made all things! If God is good, how can evil exist and why does he allow it?
This article, 'A Good Reason For Evil', is one of the best explanations I've come across. It also enlightens Christians, about the attitudes they should have, when bad things happen to them.
Stand to Reason: A Good Reason for Evil