Aaron Burr was charged with a conspiracy. I think the true aim of that conspiracy has never been determined with absolute certainty. However at its grandest, the plan may have been for Burr to make a massive new nation in the west, forged from conquered provinces of Mexico and the states west of the Appalachian Mountains. Burr was to have been the leader of this Southwestern republic.
Quite ambitous if you ask me.
I wonder sometimes how the world would look today if indeed such a state had been founded, or if the United States had broken appart on other ocassions (Civil War) or if Texas had never joined the US. There is much room for speculations.