Most of this discussion involves events at the end of Harry Potter and the Deathly Hallows so if you haven't read that book and don't want spoilers, then stop reading right now.
After Sirus died, when Harry was trying to sort through what happened and deal with his death, he went to Nearly Headless Nick to ask him about death. Nick told him that ghosts were those who did not go on and take that final step, but that he doubted Sirus was a ghost or could come back because Sirus was brave enough he would not have stopped and tried to come back.
After Voldemort killed Harry, and Harry was not fully dead (and was talking with Dumbledore), he was in limbo. He was given a choice to go back and fight Voldemort or to go on.
If Harry had not made a choice, would he have become a ghost, existing between the living and the dead?