Some bands always sound fresh because their sound is so unique. Steely Dan, for instance, fits that description. Traffic certainly also qualifies. Here are The Low Spark of High Heeled Boys, Dear Mr. Fantasy, Freedom Rider and Glad.
The rock-and-roll song with the most unique genesis probably is John Barleycorn Must Die. This site has two versions of the lyrics. The song — which could have been called John Barleycorn Must Die in a Sickeningly Painful and Violent Manner — is not your average hit record:
Although written versions of the song date back to the reign of Queen Elizabeth I, there is evidence that it was sung for years before that. There are a number of different versions, but the most well-known one is the Robert Burns version, in which John Barleycorn is portrayed as an almost Christ-like figure, suffering greatly before finally dying so that others may live.
Wikipedia suggests a method to the mayhem:
John Barleycorn in the song is a personification of the important cereal crop barley and of the alcoholic beverages made from it, beer and whisky [sic]. In the song, John Barleycorn is represented as suffering attacks, death and indignities that correspond to the various stages of barley cultivation, such as reaping and malting.