Not just a song that can be found in the archives, but one that almost everyone can hum, even today.
(Somebody asked what was meant by "today's...." Throw whatever you want out, somebody tossed out "Love me tender" as being a tune from in the 1860s.)
Fly me to the Moon - Frank Sinatra
Simple, yet very recognizable melody. Easy to whistle, but could also be extended to a whole orchestra with vocals.