In Henry James's 1898 The Turn of the Screw, the audience is never sure if the ghosts of Peter Quint and Miss Jessel really exist or are just a figment of the narrator's imagination.
Since she is the lens through which we see the entire story unfold, we have to accept her sightings of the ghosts as the only real evidence of their existence. However, we are never given enough information about the narrator's background and her psychological make-up to really know for sure. All we are given is her account against the children and Mrs. Grose, all three of whom fail to believe the ghosts exist even when they are in the narrator's presence during one of her sightings.
In the 1961 film version, The Innocents, directed by Jack Clayton, there is never a question about the ghosts' existences. Since it was an adaptation of a ghost story for the big screen, the writers evidently felt that the ghosts, as depicted by Peter Wyngarde and Clytie Jessop, had to exist. As far as adaptations go, this is probably a wise decision because the audience would be upset if they went to view a film about ghosts in which there were no actual ghosts involved. If the ghosts were not real in the film, the screen writers would have had to completely change the original story in order to explain how and why the ghosts are just a figment of the narrator's imagination. However, I believe this is a bad interpretation of the original story and takes away from what could have been James's intention.
I believe that the ghosts are actually a figment of her imagination caused by her paranoia upon arriving at Bly to be a good governess to the children. She knew they had been through a lot in their short lives because they were surrounded by people who were not related to them at the orders of their legal guardian, and she felt sorry for the position they were in. She felt they needed to be loved, so she was extremely overprotective of them, especially after she heard the stories of Peter Quint and Miss Jessel.
The main reason I believe that the ghosts are not real is the children's reaction to them. When the ghost is across the pond from Flora, she does not even pay any attention to it. A child at that age would be scared just at the mere mention of a ghost, and easily terrified if she were to actually see one in person. A child's imagination is so rampant, after the slightest suggestion of a ghost's presence, it would only be a matter of time until their head is full of nightmarish visions haunting them. However, Flora and Miles were never really scared even though the person in charge of their care was in an obvious state of panic throughout her stay. The children had always been regarded as good children, but no child is level-headed enough to remain calm while all those things were supposedly going on around them.
The governess in the novella felt that she had to be overprotective over the care of Flora and Miles. She feared they were troubled children, and she felt she had to make every necessary precaution in order to preserve their safety. She knew they were good children; but there were many things that were never explained to her, such as the previous employees of the house as well as Miles' expulsion from school, that she feared the worse for them. Somehow, this translated into her having visions of ghosts, and from there, her fears took off until we are left wandering whether or not any of these things actually took place.