Is [God] willing to prevent evil, but not able? then is he impotent. Is he able, but not willing? then is he malevolent. Is he both able and willing? whence then is evil?   —  David Hume

The passage  above from the Scottish philosopher David Hume succinctly summarizes the reasoning behind the decisions of many to adopt the position of atheism, whether they are aware of Hume or not.  In fact, the challenge posed by this short argument has rarely been answered to the complete satisfaction of many.  Theodicy is the term that has been used to denote philosophies that have attempted to reconcile God and the existence of evil.

In the Judeo-Christian tradition, God is conceived as having the attribute of omnipotence, which is usually defined as unlimited power, the ability to do whatever one wants.  However, this conception of God was not held by many ancient Greek and Roman philosophers, who saw God as being very powerful but not all-powerful.  The Roman physician and philosopher Galen argued that God was limited by necessity and matter — God could not do whatever he wanted, and this conception was different from the Jewish and Christian conception:

This is where our opinion, and that of Plato and all others among the Greeks who correctly deal with the rationality of Nature, differs from that of Moses.  For Moses, it is sufficient to say merely that God “willed” to order the universe in a certain way, and it was done.  For he [Moses] thinks that everything is possible for God, even if he wanted to make a horse or a bull out of ashes.  But we know that is not the case.  We say, on the contrary, that certain things are impossible by nature.  God does not even attempt those things, but from what is possible, he chooses the best to come about.  (On the Usefulness of the Parts of the Body, quoted in Dale B. Martin, Inventing Superstition )

In this view, the existence of evil does not pose a problem for the existence of God, because God is not all-powerful to begin with — God is simply very powerful.

In the contemporary, popular view, the conception of God as being less than all-powerful is regarded as blasphemous, ridiculous, or self-contradictory.  However, the notion of limitations on God’s power is found in a number of prominent Christian theologians, including Paul Tillich, Reinhold Niebuhr, Edgar S. Brightman, and Martin Luther King, Jr.  In fact, there is an entire school of thought known as “Process Theology,” that conceives of God as being limited in power and acting gradually on the world over time.  This alternative conception of God is not an entirely satisfactory answer to the problem of evil, but I would argue that it holds much fewer difficulties than the popular conception of a God who can do whatever He wants but chooses not to.  It is also superior to an atheism that sees the universe as being composed merely of a set of physical laws and random events with no underlying, unifying, intelligent order.