My grandfather got mad at me during the last Census (I worked in the Census office) because there was no place to check mark "American" when it asked for race. He didn't want to choose what color of skin (since Whites don't get to choose the "Cultural Background" that they identify with), just where he came from.
I like your Grandfather!
One thing about this country and a few others (such as Canada and Brazil) is that the concept of race is growing irrelevant because people who would never otherwise meet are meeting and forming families. What race are they? The human race; it's as simple as that. When I was in college quite some time ago, I was tempted to check the box for "Other," which may or may not still exist. I figured I was Jewish, which many people think of as nonwhite or at least not completely European. Tonto, I like your solution of just not filling in anything.
There's one place where race is still relevant, and it's in medicine. This is more a matter of DNA than of any other issue: certain illnesses are more prevalent in certain ethnic groups, and doctors need to be aware of things to look for, disorders to screen for, and treatments to use or avoid. An example: African American women seem to be succeptible to types of breast cancer that are harder to treat and must be addressed differently. Also, and this is still a matter for some concern, it's hard to find compatible tissue donors (bone marrow and so forth) for people of mixed race. Keep in mind that although there are more mixed-race people every day, they are of all different blends, so the genetic patterns are different. But as medical science becomes more adept at engineering these things, even that aspect of race will be less important.