My 13 yr old wants to read some horror. Or watch some scary movies. Not too scary, to start with, because the most horror-ish thing she has ever seen is Jumanji when she was much younger. Any suggestions?
The Universal (Karloff, Lugosi, Chaney) classics of the 1930s-40s, then the Hammer (Cushing & Lee) films of the 1950s-60s along with the AIP Vincent Price films of the same era. Also, the Silents- Nosferatu & Chaney’s Phantom of the Opera for sure.
Godzilla
King Kong.
THEM!
I adore THEM! I sneak it into my junior high class when we’re studying insects, and the kids love every cheesy moment of it.
I remember reading some Alfred Hitchcock short-story compilations when I was about that age, which contained most memorably the story about the boy with the super-psychic powers that sends people to the cornfield. Also “Fair Beckoning One,” I think.
You might look to see if such anthologies are still available. I think most of those stories were published in the '50s or '60s, so they’re not graphic at all.
Time for some Stephen King.
Skeleton Crew and Night Shift are two older collections of short stories.
Skeleton Crew contains The Mist - which was recently made into a movie.
Whatever you do, do not get her any of the Scary Stories to Tell in the Dark collections illustrated by Stephen Gammell. Because those illustrations will scare the poopcrap out of her.
Actually, strike that, you should totally get them for her, because they are awesome.
Something Wicked This Way Comes may be a good test. It’s rated PG.
You took my choice! 
Anything by Bradbury would be good – and The Martian Chronicles might start an interest in SF.
My daughter’s been a horror fan since forever, and she loved John Saul’s books at a young age, and King, of course.
I don’t know if King’s The Girl Who Loved Tom Gordon is exactly horror, but the protagonist, who is alone for most of the book, is a 9 year old girl.
I watched Poltergeist when I was 6 with no permanent damage. I think it’s pretty light.
I second the Stephen King for reading. For lighter things from him, I like Firestarter, Cujo, Pet Sematary, Carrie, Christine.
The Dean Koontz book Watchers is still one of my all time favourites. (It’s about a dog which makes it more approachable IMHO.)
Michael J. Fox in The Frighteners! I LOVE this movie. It has its scary moments but overall it’s a really fun movie.
Michael J. Fox) plays Frank Bannister. His character has psychic powers that he uses for a sham supernatural private-eye firm. With the help of a few ghosts (one played by John Astin as a former wild west outlaw and judge) into staging hauntings and poltergeists in the homes of potential clients. Bannister (MJF) starts noticing real hauntings around town similar to that of a serial killer from several years earlier. Bannister has to get to the bottom of the killings. There’s also a great scene or two with R. Lee Ermey as a ghost drill sergeant.
I’ll recommend Triangle, I movie I just got recently from Netflix. It’s billed as a horror movie but there are mystery and thriller elements in it. There is some violence and bloodshed but that’s not the main thrust of the movie. The main thrust is trying to figure out what is happening. The story unfolds over time and that’s the main draw for me.
So if your 13yr old is able to figure things out and likes puzzles, this would be a good movie.
J.
Thanks for these suggestions - I’ll look around and see which ones I can find.
Is Stephen King really not that scary? I read Salem’s Lot when I was 13, and I was terrified. I was scared to look out a window out night for years afterwards, for fear of lurking vampires. Maybe I’m just a wuss.
Salem’s Lot is pretty scary.
Read The Mist - and see what you think for her. It’s creepy as hell, but it’s more about the small town people interacting under stress than anything. Which can be terrifying, now that you think of it. 
I read The Exorcist at 13, though, so take my advice with a grain of salt. 
If the OP’s daughter really enjoys scary stuff, though, I think as long as movies are within the PG and PG-13 range, they should be pretty safe.
The entire Buffy and Angel anthologies are available on Netflix Instant!!
I started reading Stephen King when I was 12, and have been a horror fan since I saw Jaws when I was 8. So a 13 yo expressing interest in horror to her parents is probably ready do just dive on in!
As long as you stay away from R rated stuff, and from the gory torture-porn and Asian horror (which is pretty much R, NC-17 or unrated), she should be fine, and have plenty of material for many years. I didn’t get into the gross stuff until I was in my 20’s, and even now have to be in the mood for it, like really spicy food.
Hey, I’m 49 and King still scares the crap out of me sometimes! But as someone upthread mentioned, some of his short works, especially some of the older ones, from Skeleton Crew and Night Shift are milder. In those two collections, look for Survivor Type and The House on Maple Street; whatever you do, don’t let her read The Boogeyman until she’s at least 25!
You might try a short story anthology series called Blood Lite and its sequel, Blood Lite II (published just a few months ago). All the stories are written by members of the Horror Writers Association, most of the writers are well-known and the stories are creepy while having a humorous bent to them.
I agree with others who’ve recommended King’s “Night Shift” collection. I’d also suggest Bradbury’s “The October Country,” a collection of his horror stories published in the 1950s. Both of these anthologies are triumphs of mood and tone with really very little in the way of gore, profanity or sex.
It occurred to me as well, R.L. Stine (author of the Goosebumps series) has a teen-oriented horror series called Fear Street. Some of the books feature the supernatural, others are more “the hot boy next door is a killer” type. I’ve not read anything by Stine but Fear Street is popular with the younger teens I assist as a librarian.
Any of the old volumes of Pan Book of Horror Stories.