There are four basic types of conflict. Conflict is what drives the plot of any given piece of literature.
One prevalent type of conflict is person vs. person, in which a protagonist goes against an antagonist. A good example of this type of conflict occurs in Richard Connel's short story "The Most Dangerous Game" where the evil General Zaroff hunts men and the protagonist Rainsford becomes his prey in the second half of the story.
Another category of conflict is person vs. nature. This conflict involves the protagonist in a struggle against nature or the outdoors. An example of this conflict occurs in Jack London's short story "To Build a Fire" in which a man finds himself hiking in the Yukon wilderness in potentially lethal conditions. When temperatures reach dangerous levels the man accidentally gets wet and fails in building a fire, ultimately freezing to death.
Yet another type of conflict is person vs. society. This conflict puts the protagonist against some injustice in society. An example of this may be found in John Steinbeck's novel Of Mice and Men. Lennie is a mentally challenged character in a society that doesn't understand or sympathize with his disability. When he accidentally commits murder, his best friend George has to kill him in order to avoid a punishment by society which Lennie would not have understood.
While the first three conflicts involve external threats to the protagonist, the last type of conflict is internal, going on in the protagonist's psyche. In this conflict the protagonist struggles with his own feelings or conscience. An example of this occurs in James Hurst's short story "The Scarlet Ibis" in which the narrator struggles with the guilt he feels over causing his disabled brother's death when they were children. Several times in the story the narrator, who is flashing back to the events, comments on how prideful and mean he was to his brother.