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 (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 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.
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.
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).