For the most part, I've stayed away from the "If Sarah Palin was black" paradigm. I think that sort of thing opens you up to generalizing. That said, I found this Tim Wise piece pretty convincing:
White privilege is when you can call yourself a "fuckin' redneck," like Bristol Palin's boyfriend does, and talk about how if anyone messes with you, you'll "kick their fuckin' ass," and talk about how you like to "shoot shit" for fun, and still be viewed as a responsible, all-American boy (and a great son-in-law to be) rather than a thug.
White privilege is when you can attend four different colleges in six years like Sarah Palin did (one of which you basically failed out of, then returned to after making up some coursework at a community college), and no one questions your intelligence or commitment to achievement, whereas a person of color who did this would be viewed as unfit for college, and probably someone who only got in in the first place because of affirmative action.
White privilege is when you can claim that being mayor of a town smaller than most medium-sized colleges, and then Governor of a state with about the same number of people as the lower fifth of the island of Manhattan, makes you ready to potentially be president, and people don't all piss on themselves with laughter, while being a black U.S. Senator, two-term state Senator, and constitutional law scholar, means you're "untested."
White privilege is being able to say that you support the words "under God" in the pledge of allegiance because "if it was good enough for the founding fathers, it's good enough for me," and not be immediately disqualified from holding office--since, after all, the pledge was written in the late 1800s and the "under God" part wasn't added until the 1950s--while if you're black and believe in reading accused criminals and terrorists their rights (because the Constitution, which you used to teach at a prestigious law school, requires it), you are a dangerous and mushy liberal who isn't fit to safeguard American institutions.
The basic point here, I think, is that racism allows white people to be mediocre. In all honesty, I'm still thinking about a lot of this, and trying to see where I stand. I must be honest with you--this whole Barack Obama thing has fucked me up. We can talk White Racism all day, but I'm still grappling with the idea that this dude won primaries and caucuses in states that a lot of us always presumed were off-limits to black folks. I know that Appalachia explains a lot, but still, it didn't explain it two years ago. No one thought this was going to happen. The worst thing, I think, would be to continue to write and think like Obama didn't happen. All of that is to explain why I'm sort of wishy-washy on how race is being played out. Still, I do have trouble imagining any black person with Sarah Palin's MO being governor of anything.