Stephen King's Amazing Stories have also influenced modern horror in terms of the variety of horror themes. He explores psychological horror, supernatural horror, and horror related to human relationships. This has inspired modern authors to be more diverse in their exploration of horror, rather than sticking to a single type of horror element.
His use of character - driven horror is also a big influence. Instead of just relying on monsters, he makes his characters' fears and flaws drive the horror. Take 'Misery' for instance. The obsessed fan Annie Wilkes is as scary as any supernatural being. This approach has been widely adopted in modern horror writing.