Yes, read it, it is one of the most infuential stories in Russian literature. Doestoevsky, Tolstoy, Turgenev, and other have all been quoted as saying ``We all cam out from under Gogol's overcoat. Maybe only Dostoevsky said that, but it's believable that any of them said that.
There is actually a good companion piece to The Overcoat in U.S. literature, I believe. Read Melville's Bartleby the Scrivener.