Despite the richness of the field, there is a surprising convergence not just on the best-known book set in Russia, but on the top three spots. In order, the most widely-owned books set in Russia on both LibraryThing and GoodReads (all nineteenth-century classics) are:
Crime and Punishment by Fyodor Dostoevsky
Anna Karenina by Lev Tolstoy
The Brothers Karamazov by Fyodor Dostoevsky
At fourth place on GoodReads (fifth on LibraryThing) is a twentieth-century magical realist satire on Stalinism, written by a Ukrainian but clearly set in Moscow:
The Master and Margarita, by Mikhail Bulgakov
And on fourth place on Librarything (sixth on Goodreads, behind a bio of Catherine the Great) is my personal favourite work of Russian literature, though I suspect that its sheer size puts some readers off:
War and Peace, by Leo Tolstoy.
Bubbling under: Solzhenitsyn, Zamyatin, Gogol, Nabokov.