Well, kind of. While not necessarily *Russian*, they were composers prominent and popular during the Soviet era, and as a result were primarily associated with Russia; their works have thus become recognized as 'Russian', or at least eastern/different. They are pretty sweet IMO.
While natively Armenian, Aram Khachaturian was born in Imperial Russia, and lived most of his life a supporter of the idea of communism, a proud Soviet citizen and a distinguished composer. He combined traditional Armenian folk music with the classical senses of past European and Russian composers, creating several pieces notable to Russians and abroad during the soviet era. Khachaturian had an on-off relationship with communism, which he supported all his life, despite some conflicts with the party and with national officials.
A well known piece of Khachaturian's is his 'Sabre Dance'. From the ballet 'Gayane', the sabre dance has become a popular piece in much of the western world. You may recognize it as the music used in every movie trailer and TV show, ever, to indicate zaniness/tension or to introduce a crazy character (tied alongside Grieg's "In the Hall of the Mountain King" for most overused classical composition ever) -
Sergei Prokofiev, while born in Ukraine, was raised and lived as a Russian (Soviet) citizen, and became a well-known composer, especially of virtuoso piano pieces. Unrestrained by most musical conventions, Prokofiev's compositions made use of strange tonalities, harmonic unrest and dissonance to create an unusual, sometimes unsettling musical atmosphere. Some of his more interesting works were his operas; Love for Three Oranges is quite famous, and also of interest is his operatic adaptation of Tolstoy's War and Peace.
The March from Love for Three Oranges was a popular period piece, gaining recognition in the west; it was used in a number of radio broadcasts around the time, and I recall seeing it accompanying some of those old-timey documentary type films. It's an interesting piece.