I was stumbling around the internet today and found The Inconvenient Science of Racial DNA Profiling. Apparently some dude is able to figure out, with high accuracy, what race someone is by looking at their DNA. And this has been used at least once to apprehend a black perpetrator - this was the Baton Rouge serial killer, and he was indeed found guilty.
According to Wikipedia, the "major races" (I'm assuming the AABC here, asian/native north or south american/black/caucasian) are genetically different by a great grand total of .08%. If .08% of our genes are different, that's 8 in 10,000 genes. That's a difference of 280 genes, at most (assuming a very high value for the number of human genes, according to Science Daily, and also that every single genetic difference is in a seperate and functional gene).
I'm sure that everyone has noticed by now that it seems like the primary differentiators of the "major races" are extremely superficial. Skin color, hair color, hair texture, areas of hair growth, and facial structure seem to be a few of the notable differences. And going back to wikipedia, even one of those things (hair color) involves at least three separate melanin proteins, which are made by who knows how many genes.
On top of that, there is a mounting pile of evidence for a series of genetic bottlenecks in human evolution. A genetic bottleneck basically means that a significant percentage of the population died off, leaving a much smaller number of people around (with, presumably, a much lower genetic diversity).
You can point to the teensy weensy difference between us and claim that it represents something besides a way to easily categorize the human race if it suits you. The truth is that we are all sisters and brothers on this damn crazy planet.