Both the Mississippi and Chicago rivers have flowed backwards at various points in history, according to an article in Mental Floss. In the case of the Chicago River, human engineering prompted the reverse flow. The Mississippi has flowed backwards several times due to natural disasters.
Mental Floss reports that early settlers in the Chicago area called upon an engineer to assist them in reversing the flow of the Chicago River once they realized that the waste they were dumping into the river was making its way to Lake Michigan, which they used as a source of drinking water. The "Chicago Diversion" project of the late 1800s not only reversed the flow of the river, but it connected the Mississippi River to the Great Lakes.
Three earthquakes that struck the Louisiana Territory in 1811 and 1812 shook the ground to such a degree that the Mississippi River temporarily ran backwards, sucking boats along with it. There is no historical record of exactly how long it took for the river to resume normal flow, according to Mental Floss. However, it is known that the Mississippi reversed course for roughly 24 hours when Hurricane Katrina hit in 2005.
The U.S. Geological Survey reports that the Mississippi River also flowed backwards for about one full day when Hurricane Isaac struck in 2012.