This is from Wikipedia
The Illinoian Glacier, about 300,000 to 132,000 years before present, blocked the Mississippi near Rock Island, Illinois, diverting it to its present channel farther to the west, the current western border of Illinois.
The Hennepin Canal roughly follows the ancient channel of the Mississippi downstream from Rock Island to Hennepin. South of Hennepin, Illinois, the current Illinois River is actually following the ancient channel of the Mississippi River to Alton, Illinois, before the Illinoian glaciation.
Other changes in the course of the river have occurred because of earthquakes along the New Madrid Fault Zone, which lies between Memphis and St. Louis. Three earthquakes in 1811 and 1812, estimated at approximately 8 on the Richter Scale, were said to have temporarily reversed the course of the Mississippi. The settlement of Reverie, Tennessee was cut off from Tipton County, Tennessee, during the 1811 and 1812 earthquakes and placed on the western side of the Mississippi River, the Arkansas side. These earthquakes also created Reelfoot Lake in Tennessee from the altered landscape near the river. The faulting is related to an aulacogen (geologic term for a failed rift) that formed at the same time as the Gulf of Mexico.
Through a natural process known as delta switching the lower Mississippi River has shifted its final course to the mouth of the Gulf of Mexico every thousand years or so. This occurs because the deposits of silt and sediment begin to clog its channel, raising the river's level and causing it to eventually find a steeper, more direct route to the Gulf of Mexico. The abandoned distributary diminishes in volume and forms what are known as bayous. This process has, over the past 5,000 years, caused the coastline of south Louisiana to advance toward the Gulf from 15 to 50 mi (25 to 80 km). The currently active delta lobe is called the Birdfoot Delta, after its shape, or the Balize Delta, after La Balize, Louisiana, the first French settlement at the mouth of the Mississippi.
See also: Mississippi River Delta
I copied this from a Corps of Engineers website - you might be able to get info from this person:
Kathy Gibbs, CEMVN-PA
Chief, Public Affairs Office
New Orleans, LA