I just came across this list (from October) ranking the 'Greatest U.S. Presidents'; these things are always a bit subjective, but it seems to me that this list is dangerously Machiavellian. Any list in which Polk gets more points for gaining territory in the Mexican-American War than Arthur gets for civil service reform is a list that is not ranking according to good governance. It likewise makes no sense for Harding to be less severely penalized for massive corruption than Hoover for failure to reverse to a completely new level of economic crisis. Jackson ranks very high despite the horrors of Indian Removal, but Van Buren ranks very low for continuing and enforcing Jackson's policies. The article says the ranking was by a "panel of experts"; but everyone on the panel seems to have been a journalist. Nonetheless, the list bears similarities to the sorts of rankings you get when historians and political scientists are asked to do it.
My own view is that it's best not to think in terms of Presidents but in terms of notable Presidential accomplishments. Thus we would see why it makes sense for Lincoln to rank high (successful termination of the Civil War and the Emancipation Proclamation were very good) without overlooking the fact that he suspended habeas corpus (three times!) and tried civilians in military tribunals, which is bad. Franklin Roosevelt would be properly recognized as the man who put Japanese-American citizens in detention camps, Jackson as the man who took a beautiful Cherokee civilization that was beginning to flourish and ruthlessly crushed it, and people would finally have to at least take seriously the argument that these were massively shameful failures. Likewise, Garfield's and Arthur's work in the reform of civil service (the Star Route inquiry, the Pendleton Act), which actually and undeniably made the U.S. government more efficient and less corrupt, would be recognized for the victory for the public weal it was. And so forth through the list. Further, if the list tended hawkish -- as rankings of Presidents often do -- it would be much more directly noticeable. That would be an interesting and informative set of lists: the 100 best and 100 worst Presidential accomplishments.
(Also, although obviously construction of such lists is much more complicated, we should have more lists of great Senators and Representatives. We live in a Republic. Give Daniel Webster, Theodore Frelinghuysen, and Henry Clay their due.)