In Henry James's 1898 novella, The Turn of the Screw, the governess (Miss Giddens in Jack Clayton's 1961 movie, The Innocents, as played by Deborah Kerr), is convinced that she sees the ghosts of Miss Jessel, (Clytie Jessop) the former governess, and Peter Quint (Peter Wyngarde), the former valet and Miss Jessel's secret lover. The question on everyone's mind, though, is as follows: "Do the ghosts really exist, or are they just a figment of her imagination?" I would argue that they must be real.
One example which indicates to me that they are real is that she initially had no idea of who these people were. In both versions, she sees a man standing on the tower and assumes that he must have sneaked into the house. She sees him again before she mentions it to anyone. When she finally does mention it to Mrs. Grose (Megs Jenkins), she describes him accurately before Mrs. Grose tells her who he is. It is not as if the governess had told her what he looked like and then asked her if that was the correct description. This alone proves that she is not imagining things if she could describe a man that she had never met or had seen a picture of before.
Another example which demonstrates to me that the ghosts are real is at the end when Miles (Martin Stephens) and the governess are outside, as Quint appears. Miles does not actually seem to see him, but we know that he has seen him before or at least believes that he is there because he speaks to him. He calls his name and then calls him a devil. This shows that Miles knows he is there because the governess has not mentioned his name before that. This shows that there is some presence there even if she is the only one that can see it. It is at least felt by someone else.
Lastly, in the movie, when Miss Giddens sees Miss Jessel in the schoolroom, she is crying. When Ms. Giddens goes to the desk, she sees the tear stains on the papers that were on the desk. If that is not a real ghost, I do not know what is.
While it was Mr. James's intention to make the reader question whether the ghosts were real or not, there is plenty of evidence in the book as well as the movie that suggests their reality. There is also evidence that supports the opposite. This is the beauty of this novella and its cinematic adaptation. For the mystery buffs, there is mystery; and they can choose to believe that the ghosts are real; but for the skeptics, they can choose to believe that the ghosts are not real and still enjoy the story.