Russia's creative output seems to me to have been disproportionately large in the last ~150 years. Consider :
   Writers                            Composers
 Aleksandr Pushkin                Aleksandr Borodin

 Nikolay Gogol                    Modest Mussorgsky

 Ivan Turgenev                 Nikolay Rimsky-Korsakov

 Leo Tolstoy                     Peter Ilich Tchaikovsky

 Anton Chekhov                  Sergey Rachmaninoff

 Maksim Gorky                     Igor Stravinsky

 Mikhail Bulgakov                 Sergey Prokofiev

 Boris Pasternak                Dmitry Shostakovich

 Alexander Solzhenitsyn

 Joseph Brodsky

 Fyodor Dostoyevsky                  
Not forgetting the Ballet Russe and Sergey Diaghilev and Vaslav Nijinsky.
This seems to me to be an awful lot of very high-profile creativity for one nation.

Even if you take into account its population of around 150 million,it still seems quite a lot. Perhaps a country that had a system of institutionalised hardship might expect this, however, people are more inclined in such a situation to create work criticising the status quo with varying degrees of subtlety. Another factor might be the lack of availability of mainstream entertainment media and other luxury distractions that others take more for granted. Stifling of freedom of speech, something that's been fought for so hard for such a long time, would also enrage more strongly morally minded people to express themselves creatively. As Professor Pi points out, many athletes, ballet dancers, and musicians would have been highly motivated to succeed by the prospect of escape (however brief) under the Iron Curtain.