The American Civil War is a popular point of divergence in English-language alternate history fiction.
Less common variants include a Union victory under different circumstances from actual history, resulting in a different postwar situation; black American slaves freeing themselves by revolt without waiting for Lincoln's Emancipation Proclamation; a direct British and/or French intervention in the war; the survival of Lincoln during John Wilkes Booth's assassination attempt; a retelling of historical events with fantasy elements inserted; the Civil War never breaking out and a peaceful compromise being reached; and secret history tales.
The point of divergence in such a story can be a "natural, realistic" event, such as one general making a different decision, or one sentry detecting an enemy invasion unlike in reality.
It can also be an "unnatural" fantasy/science fiction plot device such as time travel, which usually takes the form of someone bringing modern weapons or hindsight knowledge into the past.
American Civil War alternate histories are one of the two most popular points of divergence to create an alternate history in the English language, the other being an Axis victory in World War II.