Background

This story originates back to 1550 in the Aztec city of Tenotchitlan which has been a part of history for over 500 years. (Hereijgers).  The popular legend of La Llorona is about an Aztec goddess formerly known as 'Cihuacoatl'.  (Santistevan).
However, there are many versions to this legend and growing up on a bordertown across from Juarez, Mexico the tale that was told different from my research.  Fortunately, I did find someone from El Paso, Tx (which is where I grew up) and she shared the same frightening tale that I grew up believing. (lostdestinations). All the stories range depending on where you grew up, but the entire story focuses on  a poor woman known as "La Llorona" who killed her children in the river. 

Sources: 
Santistevan, Bernadine.  "La Llorona." 2000-2007. Web. Oct. 19, 2010. http://www.lallorona.com
Hereijgers, Hans. “The Legend of La Llorona.” Feb. 1, 2001. Web. Oct. 20, 2010. http://suite101.com
"Lost Destinations: Tales of the Lost." 2003. Web. Oct. 19, 2010. http://www.lostdestinations.com