I cannot really think of any specific privileges that they get. Not in the US, anyway. If you call being promoted a privilege, then I would say that this group does tend to get promoted at a greater rate than others. Almost all of the CEOs of large companies are white upper class men. Almost all the wealthiest people in the world are white men.
Here in the US, I think white upper middle class to upper class women are probably the most privileged at this time. I say this because of the entitlements, at corporations, at universities, and in family court.