Missouri lays claim to the World's Largest Pecan, Rocking Chair, Fork, Goose, and Ball of String as well as a number of giant pink elephants. My favorite Missouri Big Stuffs are the World's Largest Shuttlecocks, one of which is pictured above. There are four of them that are scattered on the grounds of the Nelson-Atkins Museum of Art in Kansas City. They were created by Claes Oldenburg and Coosje van Bruggen, the same people who brought us the Spoonbridge and Cherry at the Minneapolis Sculpture Garden. See the map.
If your favorite Missouri attraction is missing, please let me know.