Henry Adams and Samuel Eliot Morison say yes. Milton Lomask says no. Gore Vidal says that Burr was a charming scoundrel, leaves the question of treason unanswered and implies that charm is underrated and that our horror before things like treason is perhaps sometimes overblown. Vidal also implies that Burr, whose only legitimate child, his daughter Theodosia, died childless, had many illegitimate children, that among these were President Martin Van Buren, and that the number and accomplishment of all of his descendants might be incalculably huge. Lomask is convinced that he had at least a few children besides Theodosia.
The charge of treason against Burr is that between 1804 and 1806 he made plans to separate the territory of the Louisiana Purchase (made in 1803) from the other United States and to form from it a separate country over which he, or he and others associated with him, would rule.
One thing not well-known today, relevant to Burr's case, is that is was not universally assumed at the time that the Louisiana Purchase, or any other land west of the Mississippi River, would permanently remain in the possession of the United States.
Burr did engage in some land speculation in the area of the Louisiana Purchase, but so did many others, and there was nothing illegal about it. He met with the newly-installed commander of the American military in New Orleans, James Wilkinson, who testified at Burr's trial in Richmond, Virginia in 1807. It was suspected at the time, and the suspicions have not lessened since then, that Wilkinson's testimony against Burr was false, and greatly exaggerated the suspicious nature of Burr's activities in order to divert suspicion away from himself. Burr was found not guilty at his trial, and Wilkinson, although he had not been on trial, was removed from his command post at New Orleans, and suspicions of one kind and another surrounded him until his death in 1825, when it came to light that he had been a secret agent paid by the court of Spain. Opinion is significantly more unanimous that Wilkinson was a bad guy and a traiter, than in the case of Burr.
To return to Burr: in 1804, while Vice-President of the United States, he shot and killed the former Secretary of the Treasury Alexander Hamilton in a duel. Many people throughout the United States were outraged by the incident, and would have liked to have seen Burr tried for murder, but it proved impossible to press any charges related to the duel against him. Those who say that Burr was innocent of any treasonous acts in the Louisiana Territory have, it seems to me, a very reasonable explanation of his trial for treason when they suggest that it was the death of Hamilton which upset people above all, and led to Burr's reputation as a monster, and to the attempt to punish him for something.
Just as in the questions of Burr's parenthood and his treason, accounts of his duel with Hamilton vary greatly. One version of the story which was popular at the time said that Hamilton fired his pistol into the air, and then stood there while Burr gunned him down in cold blood. It is said that Burr heard this version of things and said that if Hamilton had acted that way, it would have been contemptible. I have also heard that Hamilton received a great number of challenges to duels, so many that by the time of his duel with Burr, it would have looked very bad for him in his and Burr's circle of gentleman if he had turned down one more challenge.
I just found out today that the version of the duel where Hamilton fires into into the air before Burr kills him is the one portrayed in that extremely, extraordinarily, immensely popular Broadway musical about Alexander Hamilton. Which is why I'm here right now.
I'm not sure why I care about Aaron Burr's reputation, but it seems to me that the guy still can't catch a break.