"Ride of the Valkyries" is the opening movement of Act 3 of German composer Richard Wagner's opera Die Walküre. The piece is best known for its use in the film Apocalypse Now, during the scene where the American helicopters bombard a Vietnamese village. Despite the film's anti-war stance and negative portrayal of this act, Ride of the Valkyries has come to be commonly associated with one-sided and triumphant battle scenes.
There is another reason for this piece of music symbolizing war and destruction: during World War II, the Ride of the Valkyries was used to accompany several editions of Die Deutsche Wochenschau, the German WWII newsreel, featuring sequences of Luftwaffe bombings.
In Watchmen, Ride of the Valkyries is mentioned in the first section of Under the Hood. In that passage, Hollis Mason states that "no one else on Earth has to brush away a tear" when they hear that music.
In the movie, "Ride of the Valkyries" is actually heard during the Vietnam flashback scene, which shows Dr. Manhattan obliterating Viet Cong soldiers with his godlike powers. Its purpose here is obviously to serve as a shorthand reference to Apocalypse Now and all that it symbolizes.
In the world of the Watchmen, it is unlikely that Apocalypse Now was ever made, as the making of that film was very much predicated on America's failures in Vietnam, while in Watchmen's alternate history, America won a clear and decisive victory in that War.