Vulcan Ambassador Sarek and his wife, Perrin, were fond of Mozart's music, as both attended a concert performed aboard the Enterprise-D in 2366. (TNG: "Sarek")
Oddly enough, one of the pieces at the recital was actually by Johannes Brahms.
In 2368, Data listened to Mozart's "Jupiter" symphony in C major in order to analyze its aesthetics. (TNG: "A Matter of Time")
Captain Picard enjoyed performing chamber works by Mozart on his Ressikan flute. His Picard Mozart trio featured the addition of his flute composition to a previous Mozart work. (TNG: "A Fistful of Datas")