Democratic Presidents that had 2 full terms in the 20th Century: Wilson, F. Roosevelt, Clinton. (Truman's 1st term was a fill-in for FDR, Johnson's 1st term was a fill-in for JFK, Carter wasn't re-elected.)
Republican Presidents that had 2 full terms in the 20th Century: Dwight Eisenhower, Ronald Reagan. (McKinley died in office, T. Roosevelt's 1st term was a fill-in for McKinley, Harding died in office, Coolidge's 1st term was a fill-in for Harding, Hoover wasn't re-elected, Nixon resigned, Ford's only term was a fill-in for Nixon, G.H.W. Bush wasn't re-elected.)
Wow, those lists are surprisingly short, even when allowing McKinley and Clinton, whose times in office extend outside the 20th Century.
An interesting fact: 1928 was the last time the Republicans won the White House without a Nixon or a Bush on the ticket.