Though only a fraction of his work has been translated into English, Edogawa Rampo is a writer whom many fans of the weird tale would do well to read. Though primarily a mystery writer (he even has an award named after him) Rampo also wrote a number of very chilling short stories. His collection, The Human Chair, is an excellent mix of psychological horror, supernatural horror, and flat-out weirdness. The title piece is expecially good. It's such a simple, odd, idea, and the absence of any hint of the supernatural renders is all the more chilling. Only the ending lets it down, and unfortunately lets it down quite badly. Nonetheless, it's a piece I've read and reread a number of times, and remains a favorite to this day. The other pieces range from tales of torture and mutilation, to warped murder mysteries and supernatural encounters. The Caterpillar, and the Hell of Mirrors are both first-rate.
For lovers of dark psychological horror-fantasy, Stefan Grabinski's The Dark Domain merits a place on their shelf. Largely ignored in his lifetime, Grabinski quietly continued to write his 'psychofantasies' (as he termed them), oblivious to the trends of fashion or literary style that continually forced him to compromise or perish. Grabinski chose to perish, dying at the relatively early age of 49 in poverty and in pain. Thankfully, a cadre of friends and admirers kept his work alive, and as a result of this he is now available to read in English. The pieces themselves range from tales of persecution and paranoia (Stabisimus, The Glance), paranormal obsession (The Area, Szamota's Mistress), quasi-philosophical horror fantasy (Saturnin Sektor), to straight forward Gothic horror (Tale of the Gravedigger). There are also a number of very fine train stories of which The Motion Demon is perhaps the best.
The Decapitated Chicken by Horacio Quiroga contains some of the most brutal, uncompromising horror pieces I've ever come across. Although primarily non-fantastical, most of the tales here are set in an environment so alien to Western experience (the South American jungle) that they have the effect of removing the reader from safe, familar terrain and thrusting him into a world of dangers as chilling and as unknown as any in more overtly fantastical fiction. Quiroga led what was by all means a terrible, tragic life, and his writing reflects this. Here is a world where there is no redemption, only death in its many forms. The title piece, about four mentally retarded brothers and their gradually more sinister relationship with their sister, is utterly unique, and quite brilliant. Tales of talking dogs, living pillows and unmerciful work gangs make up the rest of the collection.
Though not a horror writer, Borges wrote a number of tales that could quite conceivably fit into the genre. Tlon, Uqbar, Orbis Tertius is an excellent piece: the history of a secret, worldwide movement to bring into being an alternate Earth, and its accidental unearthing by a duo of scholars flicking through an obscure copy of the Encyclopedia Britannica. The Immortal, The God's Script, The House of Asterion and There Are More Things (this last dedicated to Lovecraft) are all superb.
Whilst I'm on the subject of Latin-American writers, Julio Cortazar's short stories are well worth looking into. The Idol of the Cyclades and The Night Face Up are both expert blendings of horror and fantasy. They can be found in his collection Blow Up and Other Tales.
Ryunosuke Akutagawa might be known today primarily for having written the piece, or pieces, on which Akira Kurosawa's acclaimed film Rashomon was based, but he also wrote a number of other accomplished short stories of which The Hell Screen is perhaps the best. A brilliant but depraved artist is commissioned to produce a folding screen depicting various scenes of Hell for a Lord of the Japanese Court. The lengths to which he will go to make his work as realistic as possible lead inevitably to disaster... Akutagawa himself, a distured young man, compitted suicide at 35. Some of his later stories, Spinning Gears for example, are heartbreaking in the horrendous emotional despair they convey. Not strictly horror, but then not exactly comfortable reading either...
Kobo Abe's reputation lies mainly on two novels: The Woman in the Dunes and The Face of Another. In the first, a bug collector comes across a strange village falf-buried in the dunes. He soon finds himself a prisoner of the villagers, forced to dig away the sand which daily threatens to submerge the entire village. In the second, a man horribly disfigured in a scientific accident, creates a perfect mask whose imagined personality he gradually comes to identify with.