Why does the Old Testament never mention unclean spirits and demon-posessed people? Why does the Old Testament never mention unclean spirits and demon-possessed people? Or I am missing something?
You're missing something.  :)

1 Samual 16:14:


  Now the Spirit of the LORD departed from Saul, and a harmful spirit
  from the LORD tormented him.


Then he started playing a game of darts with David as the bulls-eye.