Wilson, Roosevelt, Carter, Reagan, Clinton
In the twentieth century, those were the five men who defeated a sitting president on election day in November.
One immediate fact worth noting: they were almost all two-term presidents (or, in Roosevelt's case, over two terms). Jimmy Carter is the only exception, and he has the unique distinction of defeating a sitting president (Ford) who was never elected to either the office of the presidency of the vice presidency---and even that victory was very marginal. So in some ways he's the exception that proves the rule.
All five were governors, and Reagan and Carter were the only non-sitting governors at the time of their electoral victories.
At least three of these men had pivotal presidencies. Riding the high tide of Progressivism, Woodrow Wilson expanded federal powers and charted the nation's entry into World War I and the resulting peace. Franklin Delano Roosevelt in many ways created the modern regulatory state and the imperial presidency; after recasting the federal government during the Great Depression, his administration laid the groundwork for the new global order in the aftermath of World War II. Ronald Reagan drew on simmering resentments against this modern regulatory state in order to revise it, and his foreign policies helped break a Cold War that had dominated global politics for decades. It is perhaps too close in time to evaluate the ultimate significance of Bill Clinton's presidency.
These facts would suggest that, if a Republican is victorious against Barack Obama in November 2012, he or she could have a chance at playing a historic role.
Having the presidency adds a kind of grandeur to a candidate, so a candidate who defeats a sitting president often demonstrates a kind of broad appeal to the public. Most of those men who have beaten a sitting president have powerful visions for reforming government and the capacity to accomplish at least some part of these visions. For the most part, these men were also able to articulate a compelling narrative for a way forward.
The political pendulum has swung very wildly over the past few cycles, and the dynamics of the past have, obviously, only a limited application for the dynamics of the future. But sometimes precedent can have its wisdom.