Game Boy
Music A
Music A has become a well-known song in its own right. It is an instrumental arrangement of a Russian folk tune called Korobeiniki.
(Start at 0:19)
Music B
Music B is an original track by Hirokazu Tanaka, the game's sound designer.
Music C
Music C is an arrangement of Johann Sebastian Bach's French Suite No. 3 In B Minor, BWV 814, IV. Menuett — Trio.
Nintendo Entertainment System
Music 1
Music 1 is Dance of the Sugar Plum Fairy, a tune noted to be scene 14c of act two of The Nutcracker, composed by Tchaikovsky.
'Karinka' (BPG/Tengen)
One song in the BPS and Tengen versions is the Kalinka (or Karinka, as referred in-game), a famous Russian song written by Ivan Petrovich Larionov.
(Start at 0:18)
Victory Song
The victory song playing while the rocket blasts off is George's Bizet's Les Toreadors from Carmen Suite No. 1.