Oh, is it too late for a SPOILER ALERT? Get over yourselves, the book's over a hundred years old! There's no excuse for not having read it already!
Of course, the main reason to read The Turn of the Screw is to decide the great question: are the ghosts real, or is the governess just crazy?
Yes, and hell yes.
To me, the textual evidence indicates that the ghosts are real. Even though she never met either Quint or Miss Jessel in life, the governess can describe them well enough that the housekeeper knows who she's talking about. Unless the governess was doing some serious sleuthing before coming down to the house, and didn't bother to mention it, there's no way she could have known what those two looked like.
Besides, the story is better when the ghosts are real. The real strength of the tale is how dry, brief, yet tightly wound her encounters with the spirits are. There's no rattling chains or blood running down the walls; the ghosts never speak, and neither does the governess. There's only the sudden encounter, always someplace vaguely precarious--a tower, steep stairs, the edge of a lake--and the mutual, understanding, yet absolutely silent stare. Bone-chillingly beautiful and perfectly executed.
I think most readers prefer the second explanation--that the governess is insane--because that makes the story more convoluted and psychologically intense. But I think in this case we can have our cake and eat it too. The ghosts are real, but the governess is just nuts. I don't mean clinically so; I mean she's a completely incompetent, sexually repressed weirdo with a Messiah complex. Oh, and she's a rotten teacher, too.
Obviously this isn't pure literary analysis, more of an emotional reaction. But after several years of teaching, I find myself wanting to drag the character out of the pages and have a little "chat" with her.
Governess: ...and then the letter came from his school and said Miles had been expelled. I didn't want to say anything, so...
Me: Wait, what? Did you ask Miles why he'd been expelled?
Governess: Oh, no! He seemed like such a beautiful little angel that I thought there must be some mistake!
Me: So you believed him instead of all his teachers and the headmaster. Right. Okay, what did his uncle say when you contacted him?
Governess: Oh, I didn't! Their uncle said he didn't want to be disturbed with their care in any way.
Me: So you handled the situation yourself? Punished him appropriately, made sure he learned his lesson, and then got him into a new school?
Governess: Oh, no! I never punished the darling little things. Not even when Miles sneaked outside the house at night, just to "show you that I could be bad!" I just tucked him back in and kissed him good-night.
Me: Wait, wait--your student was wandering around outside at night and you didn't do anything about it? Not even a scolding?
Governess: Nope, not a word! And I didn't find a new school for Miles, either. He seemed so content playing with me and his little sister in the house. Besides, those terrible ghosts were after them, trying to lure them into evil!
Me: How were they trying to lure them into evil?
Governess: I really don't know, but I'm sure it was happening! My darlings needed me to protect them. I had to be with them every moment, watching their every move!
Me: Didn't Miles get tired of all this eventually?
Governess: Yes. It was terrible! He threatened to talk to his uncle, and insinuated that he was going to get me in trouble for not putting him in a new school! I was so distraught that I abandoned them at the church and raced home, intending to resign immediately.
Me: Wait, what? Your student gets a tiny bit uppity with you for not doing what you damn well know you should have done in the first place, and your response is to freaking run away and quit?
Governess: It was, but I didn't! I stayed with them until the bitter end, and at the very last I reclaimed Miles's soul from those horrible demons.
Governess: By making him tell me what he'd done to get expelled.
Me: ...you mean the thing you should have done at the very beginning of the book? The thing that would have been the completely obvious response to getting that letter from the school? That thing?
Governess: Yes. But poor Miles! When he'd confessed his sin he couldn't see the ghosts any more, and his heart broke from sheer disappointment.
Me: I'm sure he was sad...
Governess: He died that very moment.
Me: What the fuck?! Your ten year old student dropped fucking dead in the middle of a conversation?
Governess: Yes. It was truly tragic. But the important thing is, I saved him!
Me: What was he even doing at that school?
Governess: Well, nobody ever states it outright, and there's all kinds of guesses as to how, exactly, the ghosts corrupted the children. But I think what happened was that Miles learned about sex, and he talked about it to some of his friends at the school.
Me: What. The fuck.
Governess: I know! So unnatural!
Me: HAVE YOU EVER EVEN MET A CHILD BEFORE.
The Turn of the Screw. Great ghost story. Terrible teaching manual.