While I didn't find the total execution to be overall the best, Another is an anime with a good horror story core:

After a student died in school 26 years ago, the class - as a form of coping - kept acting like she was there, alive and well. They made sure her seat was kept open. They handed homework and test sheets to her, and collected them. They made sure to save her a seat on the bus for school trips. And they even left a space for her in the class photo at the end of the year.

She is standing in that space in that photograph.

The next year, though they'd assigned the right number of desks to the classroom for the number of students that year, when everybody showed up on the first day of school, they were one short. Nobody could figure out why, nor who the extra student was.

And then people started dying in mysterious and freakishly contrived ways...