John K. Sampson's "When I Write My Master's Thesis"contains a great reference to archives: "Oh the hours I spent in the archives wearing cotton gloves, shuffling photos from the night at Sanatorium..." The image of white gloves tends to draw to mind the idea of dusty papers and rooms filled with boxes, but it is definitely an archives reference in an alternative rock song.
There is actually a London, England based band named Archive. They are well worth a listen, even if the only reference to archives is their name.
Though more of a library reference than an archives shout out,the Arkells song Book Club contains the amusing line "You're my library, always open for business." Additionally, many of the Arkells songs mention well known (and at times historic) Hamilton landmarks. Some of the more well known references include the Snooty Fox, Jackson Square, Frank McCourt, and McMaster.
The "Little Boxes (In the Archives)" parody is about as archive oriented as a song can get. There are mentions of Hollinger boxes, grey boxes, folders, flattening, material types, reference, and genealogy. Check out the full song: