Not the most terrifying in terms of story per-se, Death Parade scares you deep down in your soul as various people's fates are decided while they play a variety of 1-V-1 bar games. If mortality freaks you out, this is a great addition to your anime repertoire.
Theatre of Darkness: Yamishibai
Hold-on to your teddies, because this little number packs a terrifying punch.
Set as 5-minute long episodes, these short, horror tales encompassing anything from the supernatural to the downright unsettling are sure to grab you...
Junji Ito Collection
For those either super into darker manga or just well-read, you've probably already experience some of Junji Ito's dark and unsettling works, and with the Junji Ito Collection this is something that you can now experience as animated shorts.
Based on some of his manga works, this collection animates some of his more macabre works into terrifying shorts of around 25-minutes. Just be sure to keep your table lamp on at night.
Parasyte is short, sweet and really gets under your skin. Pretty literally too for some of the characters!
When the young Shinichi Izumi has his hand overtaken by a human-devouring parasite, he has to adjust quickly and learn more about himself than he is perhaps really willing to. As a one season wonder, this is a great and easy watch for fans of both thrilling gory numbers and emotionally moving storylines.
This short but incredibly vivid anime rendition of the classic Devilman manga, Devilman Crybaby sets out to bring feelings of pressure, manipulation and paranoia to life as demons (or demon-human hybrids), and it does so perfectly.
You'll need a fairly strong stomach for gore, blood and violence for this one, but it ticks so many horror genre boxes than fans should definitely add this to their list.
So, that's our list, but what would you recommend?