Some Presidents are generally considered good, or if people can't agree on whether they were good or bad, at least historically important for good or ill. In this category one can find Washington, Jefferson, Andrew Jackson, Lincoln, Theodore Roosevelt, Woodrow Wilson, Franklin Delano Roosevelt, Lyndon Johnson, possibly Ronald Reagan - as we get closer to the present day, people can't even agree on whether a President was historically significant or not, let alone whether they were a positive or negative influence.
At the other end of the spectrum are the Presidents who are usually considered bad. In this category one can find John Adams, his son John Quincy Adams, James Buchanan, Ulysses S. Grant, Warren G. Harding, Herbert Hoover. When it comes to Presidents within living memory (basically everybody after World War II), opinion about the really bad ones is even more divided than about the good ones based on a person's political views, so I don't even want to make tentative suggestions!
Finally, there are the Presidents that are considered not spectacularly bad, but are generally considered mediocre or just plain dull. In this category one could place Presidents such as James Monroe, James K. Polk, Millard Fillmore, Franklin Pierce, Grover Cleveland, William Taft, Calvin Coolidge, Gerald Ford, and possibly George Bush Sr.
Needless to say, the presidents who are generally considered good, or at least significant and controversial, tend to get most of the attention. What about the bad ones, though? Do they deserve their lousy reputations? Even bad Presidents sometimes have good moments. Consider the first man usually considered a bad President ...
John Adams (Elected 1796, defeated for reelection in 1800, served 1797-1801)
Why so bad? As the 2nd President of the United States, following George Washington, it was almost inevitable that John Adams would be seen as lacking compared with his predecessor. Even with this huge handicap, though, he managed to do worse than almost anybody expected. During his one term as President, the United States almost got into a war with France and political hostilities reached one of the highest peaks in the history of this country, with some fearing that civil war would break out. The worst single action for which President John Adams is remembered, though, was his approval of the Alien and Sedition Acts, which targeted the political opponents of Adams' Federalist Party and in the case of the Sedition Act, was almost certainly unconstitutional. On a more personal level, Adams managed to get along poorly with virtually every single other government official with whom he worked, including his entire cabinet.
In his defense ... John Adams certainly made many mistakes as President, and was indeed a very difficult man to work with, but his greatest accomplishment is little remembered because it is something that did not happen. Adams successfully maneuvered to avoid a war with France, a war which was strongly supported by his own Federalist party, and apparently did it for the simple reason that it was unnecessary, and in his own words, "great is the guilt of an unnecessary war".
Adams never fit in well with his own party. Most of the senior Federalists owed their loyalty to Alexander Hamilton, who was considered the effective leader of the Federalist Party even though he held no public office at the time Adams became President. Adams kept all of the members of Washington's old cabinet, which turned out to be a serious mistake because they were all much more loyal to Hamilton than to him. Meanwhile, the leaders of the opposition Republican party (who are actually the ancestors of today's Democratic party, just to add a little confusion) did not realize how serious a split was developing between Adams and the rest of his party, and focused their attacks on Adams. For much of his presidency, Adams was essentially a man without a party, and he actually liked it that way, because he was the last president who tried to continue Washington's tradition of standing completely above party politics. His negotiation of a diplomatic agreement with the French infuriated his fellow Federalists, especially Hamilton, who had become second-in-command under Washington of a new army that the US was raising in case of war with France. It also baffled Thomas Jefferson, James Madison, and other Republican leaders, who had been assuming that Adams was working closely with Hamilton to push the USA into war with France. To make a very rough modern analogy, it would be kind if like if, 1 day before George W. Bush's ultimatum to Saddam Hussein in 2003 had expired and the Operation Iraqi freedom started, Bush had suddenly announced that, in cooperation with the United Nations, he had reached a diplomatic solution to the crisis after weeks of behind-the-scenes negotiating, and that now, thank God, war would be unnecessary. Try to picture the reaction from both pro-war and anti-war sides. Then multiply it at least a dozen times, and you probably have some idea of how the political world reacted to Adams' announcement that he had gotten an agreement with the French.
In 1800, Hamilton urged Federalists to oppose Adams and line up behind another candidate, and many did. This helped Jefferson win the election, although the odds would probably have been against Adams even if the Federalists had been united. How often do Presidents knowingly go directly against the policy of their own party and knowingly shoot their chances for reelection in the foot simply because they have concluded that a war is unnecessary and they must try to avoid it? Adams did, and IMHO that has to county for something.
Next ... the good side of another bad president, the son of the first one!