"Mack the Knife"

From the Wikipedia entry:

"Mack the Knife," or "The Ballad of Mack the Knife", originally "Die Moritat von Mackie Messer," is a song composed by Kurt Weill with lyrics by Bertolt Brecht for their music drama Die Dreigroschenoper, or, as it is known in English, The Threepenny Opera. It premiered in Berlin in 1928.

"Mack the Knife" was introduced to the U.S. hit parade by Louis Armstrong in 1954, but the song is most closely associated with Bobby Darrin, who recorded his version on December 19, 1958. In 1959 Darin's version reached number one on Billboard's Hot 100 and number six on the Black Singles chart, and it earned him a Grammy Award for Record of the Year.

Here is Oscar Peterson performing it:

Dick Clark had advised Darin not to record the song because of the perception that, having come from an opera, it wouldn't appeal to the rock & roll audience. To this day, Clark recounts the story with good humor. Frank Sinatra, who recorded the song with Dean Martin, called Darin's the "definitive" version. In 2003, the Darin version was ranked #251 on Rolling Stone's "500 Greatest Songs of All Time" list.

Ella Fitzgerald made a famous live recording in 1960 (released on Ella in Berlin: Mack the Knife) in which, after forgetting the lyrics after the first verse, she successfully improvised new lyrics in a performance that earned her a Grammy.