What you describe is called automatic writing. You just start writing, not knowing where the story will go, and let the characters sort of act and speak for themselves.
Paul Bowles was one author who used automatic writing for some of his work (along with his friend William Burroughs.) Check out Bowles' very good novel "The Sheltering Sky."
"The earth was made round so we can't see too far down the road and know what is coming." -- Isak Dinesen, Out of Africa