Someday by Isaac Asimov manages this with no violence, no gore, no monsters, and no clear explanation of the title. Two kids own a low-quality robot that can tell fairy tales, and listen to some of its stories while discussing how crude it is compared to most modern machinery. Very little of what they're describing is advanced far beyond the present day. Then they leave the room, and the robot tells itself a story, one about a robot taken care of by cruel "step-people," a robot that one day hears the step-people talk of how advanced robotics is getting, and who knows now that someday... and that's when the robot seems to break down, for it keeps repeating the same word over and over. "Someday. Someday. Someday."
This book cover from the Lucky Starr novels. Even now, it still sends chills up and down the spine. Book publishers should really run their covers by a few people first before mass-marketing them.
All the Troubles of the World. Panic ensues when a young boy manages to get past all the defences protecting Multivac, the supercomputer which basically runs the world. He doesn't have a sinister purpose though- he just wants to help his arrested father, and Multivac told him how to do that. The way to do that... includes destroying Multivac. Consider; A supercomputer upon whom all the economics, law enforcement, and, potentially, medicine, depend... is suicidal.
The ending of Nightfall. A short eclipse and the revelation that the humans' solar system is not one of dozens, but millions in the universe (as it is visible to them) is sufficient to drive humanity mad to the point where they will literally burn down their civilization out of fear of the darkness. The scientists try to avert this apocalypse and fail entirely.