Dramatic conflict is an absolute necessity in any form of storytelling. It posits the challenges and obstacles which the principal characters must confront, and details the means by which they overcome them (or in some cases, fail to overcome them). Without conflict, there is no story (nothing would happen). More importantly, without conflict, the characters themselves would not grow or change. Not only does conflict thus make for good storytelling, but it helps stories mirror the human condition, by which all of us grow and change as we move through life. Literary experts have broken dramatic conflict down into several different types.
Man Vs. Man
The simplest kind of storytelling conflict is man vs. man. One person sets out to achieve certain goals, while another person or persons stands in his way.
Man Vs. Nature
Man vs. nature (or man vs. God) posits a central character against the forces of the wilderness. He must survive in the woods, endure a shipwreck or otherwise confront the challenges of the natural world.
Man Vs. Society
Man vs. society conflicts array the characters against large social conventions or traditions. A woman who struggles to be more than just a housewife, or a young man alienated by the hypocrisy of big business, are good examples of such a story.
Man Vs. Himself
Perhaps the most potent form of storytelling conflict is a character confronting his own fears and weaknesses. A man struggling against his alcohol addiction or a king coming to grips with his own empty hubris are examples of this kind of conflict.
Combinations
Few works of literature focus solely on one sort of conflict, and the best combine numerous types into a single elegant package. For instance, Hamlet must kill his uncle (man vs. man) while silence his own doubts (man vs. himself) and bring change to the "unweeded garden" of Denmark's royalty (man vs. society).