Ransom Riggs posted 13 photographs that he believes changed the world in the January - February 2007 issue of Mental_Floss Magazine. Many of the one's he chose, I would also argue helped change American history - including the Migrant Mother photo, the Brady photo of the dead at Gettysburg, and the photo showing the killing of a Vietcong in a Saigon street during the Tet Offensive.
I was trying to think of other photos that were important to the direction of American history and the first one that sprang to mind was the photo of the bodies of the women who jumped from the Triangle Shirtwaist Company to avoid being burned alive inside the factory
This photo and the incident it represented not only led to improved fire safety laws, but also strengthened the labor union movement and the desire of middle class progressive women to protect the safety and health of working class women.
I think there is something powerful about images that burns some incidents into our memory that the story or explanation of a situation by itself fails to do.