Man Versus Man
Man Versus Man is possibly the most popular form of narrative conflict. In this form, conflict arises from a direct confrontation between two people or two groups of people. "Harry Potter" is a prime example; the series centers around Harry's struggle with Voldemort.
Man Versus Himself
If the writer's protagonist is struggling with an internal problem, Man Versus Himself is the narrative conflict the writer employs. A good example is a protagonist struggling with a checkered past. The conflict is whether the protagonist can come to terms with his past to find personal growth and success in the future.
Man Versus Society
Using Man Versus Society, the "bad guy" is characterized by societal issues. "The Grapes of Wrath" is a good example of this concept; in this book, the Joads family faces all of the hardships befallen by families who lost everything during The Great Depression. The book is a comment on society and class during that time period and the struggles -- or conflict -- men and women found themselves in during that time. Another great example is George Orwell's "1984."
Man Versus Nature
Narrative conflict arises in Man Versus Nature when a protagonist faces off against natural dangers, such as storms, deserted islands and frigid landscapes. This is the "survival story." Both "Robinson Crusoe" and "The Perfect Storm" present classic examples of man versus nature, with "The Perfect Storm" having the provenance of being true as well.
Man Versus Technology
As technology changes and changes our lives, writers have explored the challenges humans face when dealing with the power and the temptations new technology presents. It can be as simple as "War Games," the story about a computer that believes a war game simulation is the real deal and nearly launches a nuclear strike against Russia, or as complicated as "The Matrix," in which men are literally the slaves of technology.
Man Versus Fate
In the complicated Man Versus Fate situation, the protagonist must struggle against his own destiny, usually predetermined. Time travel stories are often cast as this. Can the hero rearrange the course of events to ensure his parents meet and he is born? That was the narrative conflict of "Back to the Future."