I was actually thinking about this thread on my to work this morning, and realize I should, nay, must submit this song:
"What a Wonderful World" - Louis Armstrong
While this song was created more 'ignorance' about Armstrong than he probably ever could have imagined, it is still by far his most recognizable song, so I added it on here. While it is great, from what I've seen, it tends to be so identified with Louis, that people don't realize he actually made his name and legacy by becoming one of the most powerful trumpet players of all time, and fathered the 'modern' style of jazz that would be played for the next 80 years, and counting.
A cool little story about Louis... when he first broke onto the jazz seen, he went into a recording with a small jazz combo (4-5 musicians). This was a time when the band played in a room together and recorded as a group, in one continuous take. Well, Louis' trumpet playing was so overpowering and unprecedented, that he had to go into a room across the hall and shut the door in order for the his playing to be balanced with the group.