Because a story without conflict is boring, meaningless, with little power to draw us in.
I once attended a writers class where the instructor talked about what made successful books and movies. He believed the key was the way these books and movies upped the stress levels in readers and viewers, taking their stress above their current level, then resolving that stress at the end. Good conflict creates that vicarious stress and resolution, sucking us into the story and keeping us caring about these fictional characters.
One of my favorite tv shows that does a fantastic job with conflict (especially interpersonal/relationships) and upping those stress levels is Masterpiece Theater's Downton Abbey. It's about the lives of a wealthy, titled family in England during WWI and the lives of their servants. After this last episode - full of relationship strife, war, death, impediments to love and dreams - I told my husband what a big mess things had become for the characters.
And we love it. We have to keep watching until that stress is resolved. We're drawn in. We care about these people.
Have you watched Downton Abbey? What are your favorite types of conflict in books or movies (physical, internal, familial)? What other movies/tv shows or books are examples of good conflict?