If you're looking for anime similar to Fragments of Horror, you might like these titles.
Tomie Kawakami is a femme fatale with long black hair and a beauty mark just under her left eye. She can seduce nearly any man, and drive them to murder as well, even though the victim is often Tomie herself. While one lover seeks to keep her for himself, another grows terrified of the immortal succubus. But soon they realize no matter how many times they kill her, the world will never be free of Tomie.
Ruka and Rumi Kobayakawa are twin sisters in love with the same man, athletic upperclassman Katsuyuki Touma. Rumi seems supportive of Ruka's fledgling romance with Katsuyuki, until the twins are infected with a strange bacterium that transforms Rumi's personality and gifts the twins with terrifying psychic powers. Now Rumi will stop at nothing - or no-one - that gets between her and Katsuyuki, including her own twin sister...
Demons are escaping from the underworld, and causing much havoc on the population. Possessing both human bodies and artifacts alike, the demons are inconspicuously forcing people to commit murders; the demons must be stopped! The task of returning – or exterminating – the offenders lies with Enma, Kapaeru, and the talking witch hat Shapoji; can Enma and the gang banish the demons before things get out of hand?
Seven stories are told in seven very different ways. In a Dahli-esque Serengeti, a tale of a hunter and hunted unfolds. A young boy finds a useful device and is sucked into a futuristic battle. A slow-paced train ride takes two delinquent school children for a ride to the beach and down memory lane. And a baby travels through his dreams because of the ‘Happy Machine’ – amongst other tales.
Years ago, a great unholy rift opened in the center of Tokyo, turning Shinjuku into a demon-infested slum. At that time, a great warrior fought their leader, but was defeated. Now, the unholy forces reach out, targeting the one man who can bring peace to the war-torn world... a young boy must now do what his father could not--defeat the evil that lives inside Demon City Shinjuku!
At Count D's pet shop, you can acquire any form of animal, from an ordinary canary, to more.. "exotic" creatures. Made to sign a contract before purchase, Count D claims no "responsibility for actions incurred" if the purchaser does not follow its instructions completely, as results can be fatal. Patrons of this shop are able to get the rarest of creatures, but often, their purchases are coupled with demons from their past that won't go away easily.