The most common type of conflict is character vs. character. In this classic conflict type, one character, a protagonist, is fighting physically or mentally with another character, the antagonist. This type of conflict can be found everywhere, from classic Western movies in which a black-clad cowboy moseys into town and challenges the white-wearing leading man to traditional tales, such as Rumpelstiltskin, in which a king and queen fight against evil Rumpelstiltskin, who threatens to take their first born.
In some stories the conflict does not come from an outside source, but instead from inside the character himself. Often character vs. self conflict involves an internal struggle or the attempt to overcome some fear or concern. If a character is wrestling with whether or not to cheat on a test, for example, the character is having conflict with himself, weighing the magnitude of the choice he is about to make and battling internally with his decision.
When the problem that the character is facing comes form the natural world, the character must deal with character vs. nature conflict. Many stories with this type of conflict feature a character trapped in the wilderness and fighting against the elements for survival. Stories in which characters must face off against natural disasters also fall into this classic category.
When the norms or rules of society prevent a character from reaching her goals, a plot has character vs. society conflict. Many science fiction tales that feature dystopian societies include this type of conflict. For example, in "The Giver," by Lois Lowery, a 13-year-old named Jonas must deal with the repercussions of realizing that everything that he thought to be true is a lie features this type of conflict, as Jonas must battle against rules in his society that make his life unlivable.