Ring Around the Rosie
The nursery rhyme "Ring Around the Rosie" is quite popular with children. Little do they know that it is a coded reference to black-face minstrel shows. Let's look at it one line at a time:
"Ring around the rosie": Rosie refers to Eliza, a character from Uncle Tom's Cabin. It was popular for minstrel shows to contain reenactments of scenes from Uncle Tom, particularly of the scene where Eliza (whose "rosie" outlook on life leads her to believe that she can be rejoined with her son) tries to cross the Ohio River which is "ringed" with ice.
"A pocket full of posies": This is "Jim Crow," the care-free minstrel caricature of a black man who is happy despite his station in life.
"Ashes, ashes": The burnt cork used by a minstrel show's white performers to give them dark skin.
"We all fall down": A reassurance that the black people portrayed in the minstrel show will continue to be downtrodden by their "betters."
Behind the Legend
In the days before video games and television, it was popular for children to play outdoors, often with other children. One game that children used to play was called Ring Around the Rosie. The game involved neither action figures nor the recreation of movie scenes, but instead consisted of a group of children joining hands in a circle and reciting "Ring around a rosie, a pocket full of posies. Ashes, ashes, we all fall down." The children would then fall down. Apparently, in simpler time, children could think of nothing better to do.
The song arose as part of a tradition of black-face or "minstrel" shows in the American south. These shows featured white people painting themselves black and making fun of black people for the purpose of, well, making fun of black people. They often contained songs that were stereotypically associated with black people, such as "The Camptown Races," "Dixie," and "U Can't Touch This." The shows were a response to what some southerners (who were so racist that they thought Birth of a Nation was a depiction of overt tolerance) referred to as "the black plague" of freed slaves.
So yes indeed this "innocent" children's song perpetuates a tradition of racism. And if you think that's bad, you should hear what "Peter, Peter Pumpkin Eater" is really about.