USA Today has a real cool map showing the rise and fall of presidential popularity (mostly the fall) since 1945. You can plot the map all sorts of different ways to see the data from various perspectives. Having just played with it for a bit, here are some glum insights:
1. Presidents mostly end less popular than they begin unless they're Reagan or Bill Clinton.
2. Republicans and Bill Clinton are more popular at the beginning of their 2nd term than their first (but it often doesn't last). Democrats, not. (Except Bill Clinton).
3. There doesn't seem to be any correlation between popularity and historical significance (who'd have thunk).
4. The presidents with the stablest popularity (a relative term, mind you) were either mediocre with fine economies (Eisenhower, Clinton), or Reagan (who also has a reasonable economy most of the time, come to think of it, but wasn't mediocre).
5. The most popular president ever (since 1945) was Bush 2, after 9/11. He then plumetted, but contrary to accepted wisdom, he never got quite as low as Nixon. And Truman went lower even than that, if you believe it. Remember him? He's the annonymous one who stepped into FDR's gigantic shoes, set up the postwar world order, set the rules for the Cold War that eventually brought victory, and fired McArthur.