This is the basic problem to overcome in a story, the driving force. If you don't have conflict, you don't have a story. Or just a story of things happening without incident.
More than any other trope, save for the Characters who are in a conflict, this is vital to fiction. You can likely find loads of theories and essays on why this is so, but for here, just trust us. You need it.
Conflict can come in many forms. According to Arthur Quiller-Couch, there are seven kinds of conflict, creating seven basic plots (Not to be confused with The Seven Basic Plots by Christopher Booker, which articulates a theory closer to that of The Hero's Journey).
- Man vs. Man: The problem is another character (Bob needs to defeat Alice to become Class President).
- Man vs. Self: The problem lies inside the protagonist (Bob doesn't know how to express his emotions to Alice).
- Man vs. Nature: The problem comes from natural sources (Bob's town is destroyed by a volcano, or Alice is sick).
- Man vs. Society: The problem is the social environment (Bob struggles to maintain his dignity in an ignorant community after receiving an Abomination Accusation Attack).
- Man vs. God/Fate: The problem is destiny, eventuality, fate, or divine will (Bob does not want to fulfill a prophecy that he will lose his family).
- Man Caught in the Middle: Of other characters or conflicts.
- Male and Female: Quibbler-Couch was persuaded to replace the "versus".
- Going beyond Quiller-Couch's list, there is also Man vs. Machine, as in machinery. Most commonly told from the perspective of a worker being replaced by a machine.
Traditionalists boil it down to the first three, redefining "Man" as a defeatable entity and "Nature" as anything that has to be survived or changed rather than defeated. According to the three basic conflicts, a Zombie Apocalypse would thus be Man Vs. Nature. Going by this model, Man vs. Society and Man vs. God/Fate would both become Man vs. Nature, and Male and Female would become Man vs. Man (Man in the Middle and Man vs. Machine, on the other hand, could be either one depending on the plot).
Now, it seems that some fiction doesn't have conflict, but even then it's presented as a challenge, which is the third type of conflict. See No Antagonist. Of course, not every work in media needs conflict, but those tend to be non-fiction, or some episodes of Slice of Life series can also qualify. If it's a story or game, conflict drives it.
It could be said that Mary Sue stories are weak because there is no conflict in how the Sue achieves things, or that the conflict is so weak and ineffectual that it still comes across that way (as with Boring Invincible Heroes). Conversely, some works come off as weak because the conflict is too grave and appears to have no palatable solution. Like many other things, it's wise to strike a balance between the two.
Due to the breadth of this trope, any work examples should be listed in the tropes under the sub indexes.
- Contrived Stupidity Tropes (when the conflict comes from contrivances)
- Internal Conflict Tropes
- The Plot Demanded This Index
- Rule of Drama (other Rule of Index tropes are for different reasons)
- Violence Tropes