[I once started a thread called something like "Criticize your own party". Unfortunately, most people made poor attempts to actually do, such as "Democrats don't show everyone how much Republicans suck enough!"]
Since I don't know which side is the "opposing" side (I find myself more often than not opposing both parties), I'll have to do some of each. Back in time and moving forward, and avoiding obvious things like the Civil War. I'm going to stick with just presidents for now. Certainly doesn't mean everything about these presidents is awesome, just some specifics, varying widely in scope.
Democrat: Grover Cleveland was possibly the only president who actively worked to reduce the scope of the power of the presidency and consistently resist the neverending expansion of the federal government.
Republican: Teddy Roosevelt, who taught people to dream big about what this country can accomplish and to appreciate its natural beauty
Democrat: Harry Truman, who had the ballsack to do what needed to be done to end WW2
Republican/Democrat: Eisenhower then Kennedy, for spearheading the drive for the space program
Republican: Nixon, for his inroads in foreign relations with countries previously considered inaccessible.
Democrat: Obama, early in his term, had a few good foreign policy moves which showed that he wasn't the wuss Republicans tried to paint him as. Remember the Maersk kidnapping almost at the beginning of his term? He upheld the American policy of never granting hijackers their demands. Are you going to let him go? No? Ok. Pow pow pow. Done.

