I'm a huge fan of alternate history. Here's one scenario my dad and I came up with while visiting some Civil War battlefields last year:
During the 1860 US Presidential election, Abraham Lincoln is defeated by John C. Breckinridge, the pro-slavery candidate. The Civil War is, temporarily, averted.
However, in 1863, a Southern slave owner visits Boston, and brings his slaves with him. While there, he is arrested by the local authorities, and his slaves are freed by the Massachusetts government, in accordance with the state's anti-slavery laws. The slave owner sues Massachusetts, claiming theft of his property. In June of 1866, the Supreme Court rules in his favor, effectively making slavery legal throughout the United States.
This sends the anti-slavery North into a fury. In November, the Northern states declare their intent to secede from the Union, establishing the Federated States of America (commonly called the Federation), with its capital at New York City. President Breckinridge, aware of pre-1860 secessionist sentiment in the South, declines to stop them.
However, tensions soon rise between the Federation and the Union. Every free state in the Union has left, including California and Oregon. But without their votes, the Union quickly passes legislation making slavery the law of the land, even in the territories. Union troops are deployed into territories, and plans are made to bring in more states. The Federation correctly perceives this as a move designed to split their nation in two, isolating California and Oregon. In response, Californian troops enter modern-day Nevada and Arizona, clashing with the Union. By 1868, the Union and Federation are at war. While fighting is initially concentrated in the West, both sides soon decide that the best approach is to deliver a knockout blow.
We haven't figured out the details, but in all likelihood, the Federation would prevail. However, we're not sure what would happen next. Would the Federation simply claim the western territories? Or would they try to annex the Union? And if so, would they reestablish the United States, or would the Federation take its place, perhaps with the intention of making a break with the slavery-tainted past?