The recently deceased Roberto Bolano has a fairly towering reputation today. He wrote The Savage Detectives and other Pynchon-esque noir/detective style literature. He wrote in Spanish.
Many writers in the Spanish language point to Luis Borges, author of "Labyrinths", as a huge influence. He wrote early in the 20th century.
Then you've got Gabriel Garcia Marquez, also writing in Spanish. He wrote some of the most well-received and genre-defining literary fiction of the second half of the 20th century and won the Nobel Prize for literature.
I would like to nominate a personal favorite: the fourteenth-century Italian poet Francesco Petrarca, known in English as "Petrarch." Not only are his writings often immensely memorable and interesting, but they were profoundly influential on many later writers in many different countries.
I have always enjoyed the great Russians such as Leo Tostoy and Fyodor Doestoevsky. While the novels tend to be very long and involved with lots of foreign and unfamiliar names, I am always sucked into the complexity of human nature that both of these authors accomplish. Favorites: Anna Karenina andCrime and Punishment.
Unfortunately, you are going to get personal ideas about the greatest writers in the world. For each person, writers appeal to them in different ways. Not everyone will agree on the greatest writers in the world. As for myself, I think that the following authors are the greatest "non-English" writers:
Emile Zola (French)
Rabindranath Tagore (Bengali)
Viktor Frankl (Austrian)
Varlam Shalamov (Russian)
Deceased: Homer, William Shakespeare, Edgar Allan Poe, Charles Dickens, Mark Twain, Guy de Maupassant, Rudyard Kipling, William Faulkner, Ernest Hemingway. Living: Herman Wouk, Gabriel Garcia Marquez, Harper Lee, Stephen King (by financial earnings only).
Definitely check out Borges.
I would say that Anton Chekhov (russian) is one of the best.
I'm sorry I forgot to clear my question ...
I need to writers of non-English writers.
I need to specify some of the most important writers in the world,
because I will be a search on this author "Alive or dead". ... and thank you.