As President, Jefferson's greatest accomplishments were: the Louisiana Purchase, reducing the debt (even while borrowing money for the Louisiana Purchase) and beginning a 24-year reign (being succeeded by Madison and Monroe) of Democratic-Republican rule which, combined with John Marshall's Federalist rulings, formed much of the meaning of the American Constitution.
As President, Teddy Roosevelt's greatest accomplishments were: the transition of the U.S. to world power status, interventions into Latin America, ending the development/privatization of the west, and attacking big business (not part of the Morgan/Rockefeller consortium).
I would put Ronald Reagan behind Jefferson and ahead of Teddy Rossevelt. In the fullness of time, I would hope that we come to see the so-called Progressive Era as a prelude to the New Deal, and as a departure from the true course of liberal, democratic capitalism.
I am happy to see Woodrow Wilson slipping further and further down in these surveys of historians. Presidents that get us into unnecessary and meaningless wars are the worst, just as those who see us through the necessary and ultimately meaningful wars are the best.
Maybe in the big scheme of things, it is best for us for a president to be near great, because of the avoidance of war and the pursuit of freedom. In my book, Thomas Jefferson and Ronald Reagan are the greatest of the "near great" presidents.
My high school U.S. history teacher was just in love with Woodrow Wilson. I used to taunt her by pointing out that Wilson kept us out of the war...until he got reelected.
The real disappointment is Calvin Coolidge; the man was an awesome President who served less then (6) years and thus could've run for another term (he served out less than the two remaining years of Harding's terms). Reagan loved him and had a portrait of Harry Truman removed and a portrait of Coolidge put up in its place.
He was a true conservative; he was against almost all federal transfer of funds from one state to another. In fact, in irony to the events in New Orleans, I believe that there was a major natural disaster in Texas when he was President and he REFUSED to send federal money to help rebuild; since it was wrong for someone in another state to fund operations in another state (Texas).
Can you imagine Bush saying that these days?
I think Teddy Roosevelt is overrated. His run for a third term (actually second term to be elected) was what prompted Pres. Taft to run against him. Taft hated being president and knew he probably wouldn't win. But Roosevelt had become such a liability that he believed his greatest service to his country was to insure that his former friend would not be elected. Of course, we got Woodrow Wilson instead, but Roosevelt had gotten dangerous.
All these years of re-writing history and demonizing Nixon it is remarkable that Nixon still outranks Carter (the greatest ex-President, dontcha know).