You would have to give me an example of a story without conflict for me to give a good answer to your question.
I think that all stories have some sort of conflict but conflict means many things...it is not just physical fighting.
You can have a conflict of ideas or ideology
You can have internal mental conflict where someone struggles within themself.
You can have a sports story with competition between teams.
Conflict makes the story interesting to the reader. The resolving of the conflict gives the story a focus.