(covers information from several alternate timelines)
Wolfgang Amadeus Mozart was a composer of Earth classical music. A prodigy as a child, Mozart was considered by many to be among the greatest of Terran composers, having written masterpieces in every genre of his day: symphonies, operas, masses, keyboard sonatas, piano and other concertos, string quartets, and other chamber works.
A little later, a crewmember of the Enterprise-D fantasized playing the first movement of Eine kleine Nachtmusik ("Allegro") on the violin, together with three other musicians dressed in period clothing. (TNG: "Where No One Has Gone Before")
In 2366, a string quartet consisting of Data (playing the violin), Miles O'Brien (playing the cello), and two more crewmembers of the Enterprise-D (playing the violin and viola) performed the first movement of Eine kleine Nachtmusik. Picard later listened to an audio recording of the second movement ("Andante") that Doctor Crusher had made as he wasn't able to attend the concert. (TNG: "The Ensigns of Command")
Captain Picard enjoyed performing chamber works by Mozart on his Ressikan flute. His Picard Mozart trio, Program 1 featured the addition of his flute composition to a previous Mozart work. (TNG: "A Fistful of Datas")
In 2370, Doctor Beverly Crusher told her son, Wesley, about the dialogue between Captain Picard and the Traveler a few years ago and also about the comparison he had made between Wesley and Mozart. (TNG: "Journey's End")
Captain Kathryn Janeway, as Lucille Davenport on the holodeck, heard someone play a Mozart sonata in the music room of Lord Burleigh's mansion. She thought it sounded "lovely" and assumed that Beatrice Burleigh played the piece. The Lord was confused, however, as Lucy didn't play the piano. (VOY: "Persistence of Vision")