Years ago, when most organizations were based on the hierarchical business model of the Industrial Age, great leaders were those who were unemotional, rational, even mechanistic. Those days are gone. Today's leader, especially one who is in charge of a dynamic, global organization, finds himself or herself in desperate need of one key trait — self-awareness.

An organization's success today depends on such a variety of talents and skills that no one leader could possibly be gifted in...