Classic theism teaches that God is impassible — not subject to suffering, pain, or the ebb and flow of involuntary passions. In the words of the Westminster Confession of Faith, God is "without body, parts, or passions, immutable." 
It is important to note that the debate regarding the doctrine of impassibility does not center on whether God has feelings or emotions. Though some would argue for the position that God does not possess any feelings or passions, those such as Paul Helm who seek to preserve impassibility do not view God as completely apathetic. Rather, the question is whether or not God's passions are voluntary or involuntary. Does God actually react to his creation in an emotional way? Can humanity hurt God, emotionally?
The standard difficulty encountered by advocates of impassibility is that the Scripture narrative presents a God who does, in fact, react to his creation. The typical rejoinder to this is that the narrative portions of the Holy Text also present God with certain human features such as hands, eyes, etc. Surely, it is claimed, we do not accept all descriptions of God in human terms (anthropomorphisms), and as such we should be cautious in accepting the emotions and passions of God at face value.
In recent years many in the Open Theist circles have explored the various anthropomorphisms of God to discover if, in fact, they do reveal something about God, however imperfect the description may be.