We're nowhere near the Mississippi River right now. But NPR's Robert Krulwich has dug up this absolutely bonkers map, from the 1940s, which captures the migration of the river through all its jumps and cut-offs and channels. Basically, what you'll see is that the Mississippi bears a striking resemblance to the Flying Spaghetti Monster—and more seriously, that the entire map of the central United States is a relatively recent (and fragile) phenomenon.
New Madrid, Missouri, for instance, is across the river from the old New Madrid, Missouri, and, were it not for the Army Corps of Engineers, wouldn't be across the river from anything, because there's a natural cutoff further downstream; Huck Finn's Jackson Island is probably gone; in Louisiana, the Old River control system is the only thing keeping the Atchafalaya from capturing most of the Mississippi's water and relocating the mouth of the big river west to Morgan City.
Anyways, check it out.