Man vs. Man
Man vs. man is one of the most common types of conflict. The hero of the story is in conflict with a single antagonist. For example, the primary conflict in "Hamlet" is between Hamlet and his uncle, King Claudius, who wants to have him killed. The primary conflict in "Gone Girl" by Gillian Flynn is between Nick and his wife, Amy, who are engaged in a psychological war that leads to potentially deadly consequences. Conflict between two people can be a physical fight, or it can be a battle of the minds, as with Nick and Amy.
Man vs. Nature
Man vs. nature conflict pits a character or group of characters against natural forces, such as storms or animals. For example, the protagonist in "The Old Man and the Sea" by Ernest Hemingway spends days in a small boat on the ocean trying to catch a particular big fish. In "Life of Pi" by Yann Martel, a boy is stranded with a tiger in a lifeboat after being shipwrecked at sea. In stories that pit man against nature, the conflict usually reveals something about human nature, such as man's fight for life or his perseverance in the face of chaos.
Man vs. Society
Stories that pit man against society are usually about a corrupt or unjust legal system, culture or other entity. Some examples include "Brave New World" by Aldous Huxley and "1984" by George Orwell, both of which are about future, dystopian worlds that oppress individual freedom and expression. In these types of stories, one or two protagonists become catalysts for change. A larger group might form that fights for systemic change, such as rebel forces.
Man vs. Self
The only example of internal conflict is man vs. self. These types of stories focus on a psychological struggle that the character is having. For example, the young Esther in Sylvia Plath's "The Bell Jar" struggles to overcome depression and define her identity as she transitions into adulthood. Similarly, Holden Caulfield in J.D. Salinger's "The Catcher in the Rye" also struggles to figure out his identity as he moves through puberty. External sources can be considered contributing factors in these types of stories. In many stories, more than one type of conflict can be identified, such as man vs. self and man vs. society in "The Catcher in the Rye."