Whether or not it's OK to watch scary movies or shows depends on your child. Every child is different, and knowing your child is key to determining what's best for them. It also depends on the movie.
Frightful fun & beyond
Some are movies are just spooky. Gentle thrills can let kids explore fears in a safe environment. Others movies can be very scary and even violent. Scary movies that contain violence or adult content can have harmful effects on young viewers' behavior and mental health.
Check the rating
When deciding if a movie is suitable for your child, a good place to start is by looking at the movie's rating. A movie rated "G" or "PG" may have spooky or creepy content, but it is generally approved for all audiences. Movies with a PG-13 or R rating are likely scarier and have either more violence or adult content. (See "Age-Appropriate Media: Can You Trust Parental Guidance Ratings?")
These ratings can give you a general idea of age-appropriateness of a film, but they don't give parents any insight into a film's content. There are websites such as Common Sense Media that review a movie's content and provide a breakdown as to what your child will be exposed to while viewing the film. This in-depth assessment of content allows parents to judge for themselves if the movie is appropriate for their child.
It's always recommended to co-view movies and other media content with your children, and co-viewing spooky or scary movies is a particularly good idea. When you watch a movie together, you discuss anything that may come up. You can also judge if the content is bothering your child and if so, you can turn it off.
It is not uncommon for scary movies to continue to bother children even days after viewing them. They may even have nightmares about it. If your child has seen something that has upset or scared them, the best thing you can do is sit down and discuss it with them.
Talk with your child
Remember that although some children may be perfectly OK with spooky content, others may not enjoy it at all. Children can feel pressured into watching a horror movie if they are with a group of friends.
Discuss your family's rules with your child. This includes how to handle a situation if, while at a friend's house, a movie is chosen that they aren't comfortable with watching. Remind older children, who may be more likely to feel pressured, that there are many adults who don't enjoy scary movies and that viewing them is not a rite of passage.