The answer: Abraham Lincoln. There can be no serious dispute.
I begin by noting that this is an obviously old-fashioned and unscientific sort of question, the kind that admits of no empirical answer. Consequently, answering it reveals more about the respondent than about the topic supposedly under discussion. Nevertheless, I think there are common enough views about what makes a successful president, and I think the reasoning here is important enough to publicize, that I will answer it anyhow.
Who are the other contenders? I assume the list is short. Only the top ten percent should be seriously considered for the title; rounding up to the next whole president, that gives us five: Franklin Roosevelt, Theodore Roosevelt, Dwight Eisenhower, and George Washington.
I am aware that I am ranking Eisenhower much higher than his consensus position at something like 10th. But on the other hand, can we really accept Kennedy, shorn of his mystique, as being at the 90th percentile or above? As for Truman, the gap between contemporary and contemporaneous judgment is so wide as to suggest that one or the other camp has got him completely wrong, and although there is much to be said on Truman's behalf I am privately convinced that Trumania is a product of the fact that he has had a very good book written about him from which practically everyone is drawing their opinion. Eisenhower, by contrast, scores low because few people appreciate his particular genius--Fred Greenstein seems to have gotten it mostly right, as did Steven Amrbose's sources--for making far-reaching moves while appearing all but tranquil. I think the present situation in Washington, with our modern-day Birchers and Brickers, suggests that Eisenhower, although "conservative," had a special obligation and a special talent for keeping nuttery out of the GOP. Moreover, any right-wing president who opposes military (although, alas, not covert) solutions for everything and takes care to ensure that the writ of the Supreme Court runs everywhere, including in Orval Faubus' state, is doing something that left-wing scholars may not be able to fully appreciate.
Theodore Roosevelt is an obvious candidate for the top five, but he lacks the crowning accomplishment--or, what is more accurate, the supreme test--that would allow us to discern exactly what fraction of his talents he exercised in office and whether they would have matched the time. Despite his evident appetite for adventurism and statecraft in the Machtpolitik sense, Roosevelt was also the most sensible and even-handed Progressive president a Republican could dream of; the perversions of power embraced by the Wilson presidency--the fondness for racism, the flirtations with dictatorship, the obsession with moral purity--only serve to highlight how effective the first Roosevelt's approach to power was.
The case for Washington as one of the greatest--although, I think, not the greatest--Americans is easy to make. The case for Washington as a great president is surprisingly hard, and in the end it rests on much the same foundation as the case for Lincoln: He upheld the rule of the federal government. Yet Washington's presidency was too concerned with precedent-setting to make it the greatest presidency; and, after all, the scope of the presidency in those early days of the Federal Republic was simply too small to allow for anyone to ascend to real executive greatness, except maybe for Alexander Hamilton. In fact, it says something about Washington that, save Lincoln, he is the only president before 1900 whom you could even consider for the top five without blushing. (I leave the scholars' rankings of Jefferson as a consensus number four pick as a weird, and rare, example of left-wing Founding fetishism.)
By elimination, then, we have FDR and Lincoln. And FDR has a very strong claim. First, of course, he is the most successful American politician ever: five national tickets, four wins. Only one other president (Nixon) comes close (five national tickets and four wins)--but two of Nixon's victories were as vice president, while all of Roosevelt's wins were as president. Furthermore, FDR has both the most impressive domestic policy record and the most immediately globally consequential foreign policy of any president. So, that's something, too.
But FDR's weaknesses are the key. The familiar distinction between the fox and the hedgehog misses out on the crucial point that a great leader must have both tendencies. The fox and the hedgehog themselves, of course, are only concerned with survival, and their differing strategies are geared to that single goal. Yet if there is to be a case that leaders are at all transformative, then survival is not enough. They must be hedgehog-like in knowing One Big Thing to which they move forward, and yet fox-like in moving toward that goal.
In the end, it is not clear that FDR had a well-worked out vision of what he wanted the world to look like. The inclusion of France and China on the
None of this, for Roosevelt, seemed to require going any further in moral or political thought than the cliches of the sermons in the Groton Chapel. There was nothing particularly radical in Roosevelt's thought, even though he was quite often daring in his deeds. Unlike Churchill or Stalin, his great contemporaries, Roosevelt did not know what he wanted the postwar world to be like, which is why he could be played by each of them in turn. It is this failure of the imagination that played at least a role in making the years after the cessation of hostilities so perilous.
The contrast with Lincoln could not, in the end, be greater. Roosevelt inherited a state already willing to respond to a strong-willed executive; even Herbert Hooever, albeit as Secretary of Commerce, had discovered that. Roosevelt moved in a world in which mass media allowed the incumbent in the White House to shape public opinion in a new way, as even Calvin Coolidge had understood. And, most of all, the revolutionary situation Roosevelt encountered could be ameliorated through existing constitutional channels--although it is to FDR's everlasting credit that he understood that there was a crisis that had to be addressed.
Lincoln could rely on none of these advantages. The White House staff did not exist, and the federal government was not much more muscular; the press was partisan and local; and the constitutional machinery had been broken from the moment of his election. Lincoln, then, had to both fix the situation at hand but also do so in a way that would serve a greater vision of what the Union had to be, and what a commitment to political liberalism meant. For, in the end, Lincoln is the closest that the United States (indeed, perhaps any major democracy) has had to a moral philosopher in high office. He was radical, for his vision of the obligations of democracy cut to the literal root of what self-governance by free people meant.
And Lincoln is personally greater than FDR, too. FDR was a traitor to his class, but Lincoln rose above his roots. FDR could condescend to understand the sharecropper and the day laborer; Lincoln had, in essence, been both. It is not sufficient for a good president--or any other leader--to have empathy for the "common man," but it is probably necessary for a great leader to do so.
Thus, Lincoln. It is a provincial choice, in the sense that I would wager that Lincoln is probably the American political figure least understood outside of the United States (what foreign policy accomplishments did he have? and how can a non-American really understand our continuing fascination with the Civil War?), but nonetheless he remains a singularly consequential figure.