"The Nose" (1835-6) by Nikolai Gogol
"The Nose" is a famous short story by the Russian writer Nikolai Gogol (1809-1852). Wikipedia has an article about the story here. The story is about a "St. Petersburg official whose nose leaves his face and starts living a life of its own."
The Russian site Internet Library has a collection of classic stories in Russian.
Project Gutenberg has Gogol stories here.
Professor Gary Saul Morson has an article about "The Nose" here.
Bibliomania has a full text of the story in English, but is sometimes off line, so here is another link to the story.
On March 25th there took place, in Petersburg, an extraordinarily strange occurrence. The barber Ivan Yakovlevich, who lives on Voznesensky Avenue (his family name has been lost and even on his signboard, where a gentleman is depicted with a lathered cheek and the inscription “Also bloodletting,” there is nothing else)—the barber Ivan Yakovlevich woke up rather early and smelled fresh bread. Raising himself slightly in bed he saw his spouse, a rather respectable lady who was very fond of drinking coffee, take some newly baked loaves out of the oven. [Full Bibliomania text]