To be controversial, one must stir passions on both sides. The person must also, to some degree, court controversy by making decisions that a large number of people dislike. In recent history, the most controversial figure is probably George W. Bush. While Clinton, Reagan, and Nixon deserve consideration, they didn't ever quite reach the level of controversy that Bush did. Going back a bit further, Martin Luther King Jr, who is not considered controversial today, was very controversial in his time. Depending on which way History goes, the same may or may not be true of today's controversial figures.
In recent history, I would definitely say George W. Bush, for the same reasons stated. In past history, there are many others. How about Oppenheimer, the creator of the bomb? How about Alexander Hamilton and the bank? How about Andrew Jackson, about whom we still argue?
I believe that Franklin Delano Roosevelt's name should be added to the list. Although he was the only president elected four times--a fact that shows a high degree of widespread popularity--many of his progressive welfare programs were denounced by detractors who thought of them as government handouts. Our two most recent presidents also deserve consideration--Bush for incompetence and dishonesty, and Obama for his catastrophic economic decisions.
I would agree that there is no ONE most controversial person in American history. For me, it would take every person hating a single person. There, throughout history, has not been one person all of mankind has hated.
Now, if you look at someone people typically have a problem with (which would make them controversial) you could name many: MLK Junior, Malcolm X, G.W. Bush, Obama, Michael Moore. The list could go on and on.
I don't think any American History figure can be named THE MOST controversial person, because that would certainly be a subjective judgment call.
However, I would lean toward Malcom X. Many in the civil rights movement saw him as a forceful/effective voice for black power and equal rights. However, many also saw him as a hypocrite who advocated violence toward those who did not support his movement's views.
How sad that the question posted lends itself to political commentary. The above post hints at the controversial presidencies of George W. Bush and Ronald Reagan, yet does not mention the second President of the United States to be impeached for criminal conduct. One must honestly admit that all Presidents are to some degree controversial.
My vote for the most controversial American would be John Brown of Harper's Ferry fame. He is considered a hero and martyr for the anti-slavery cause by many; yet he had no problem taking the law into his own hands and slaughtering innocent people when he thought it suited his cause. No person in American history of whom I can conceive has been more villified as a nineteenth century Osama bin Laden and at the same time, memorialized as a great hero.
In order to be controversial a person has to have admirers and detractors. A controversial person must be both loved and hated. So, we have to ask ourselves what public figure has had the greatest mix of emotions attached to them.
There are many people who might qualify. For example, George W. Bush was certainly very controversial. Conservatives loved him and liberals hated him. The same was true of Ronald Reagan.
However, I will have to argue that Abraham Lincoln was the most controversial figure in US history. He had people who loved him (mostly in the North) and people who hated him and thought he was the ruin of the nation. Unlike the other two I mentioned, though, Lincoln was controversial enough that his election was the last straw that caused the Civil War to happen. That is surely the most drastic result that has come from any controversial figure in US history.