The Blue Danube was a waltz composed by Johann Strauss II of Earth in 1867.
In order to celebrate Captain Benjamin Sisko's approval of taking their analysis regarding the Dominion War to Starfleet Command in 2374, the four Augments Jack, Lauren, Patrick, Sarina Douglas and Doctor Julian Bashir held a small party. They drank champagne and danced to Strauss' Blue Danube waltz. (DS9: "Statistical Probabilities")
In late 2377 The Doctor played the Blue Danube waltz in one of his recitals. When he and Captain Janeway were abducted by aliens known as the Hierarchy, the doctor altered a recording of the waltz so that it would sound out of tune. By perfoming a Fourier analysis, Seven of Nine found out that the harmonics of the piece had been modified to imitate a warp signature. The crew was able to track the signature and thereby locate the Doctor and the Captain. (VOY: "Renaissance Man")