When I was in medical school, one rather politically active lecturer reassured us that there was more (total) genetic variation between individuals than there was between people of different races. In think she intended this as an empiric demonstration that racism is inherently illogical.
Of course, her statistic was nonsense, and we can prove it from the comfort of the armchair. Take yourself and one of this planet's other people at random, and let's call the amount of genetic variation between your genomes 'G'. (The amount of genetic variation would correspond to the total number of base pair differences in their genomes.) As it stands, 'G' is only a population average; we can increase or decrease our estimates of it if we find out more information. For instance, say that we discover that the other person is your brother. G would then be much less than average - you and your brother can be expected to show much less genetic variation than two people chosen at random, since you share a very recent set of common ancestors (your parents!).
And what if I told you instead that the other person was of a different race to you? In that case, your estimation (i.e. your best guess) should be that it would increase the value of G. Races aren't physically identical (obviously, otherwise there would be no races), and genes code for these differences. Therefore, although you have a certain probability of sharing any particular gene with someone else on the planet, the genes that code for the racial differences must be different. This is why your estimated value of G goes up. Put another way, it must be true that there is more total genetic variability between races than between individuals.
But there is a kernel of truth to what my lecturer said. She was probably misquoting a very interesting statistic, namely that most of the genetic variability between people is not as a result being of a different race. The 'race genes' are only a small subset of those that differ between people. According to one estimate, only about 7% of genetic differences can be attributed to racial differences, whilst 85% are individual variations (and the rest are ethnic or national differences). And even when all the genetic variation is taken together, as a species we are in fact rather closely related.
Of course, no scientific finding could ever justify racism of any sort. One mustn't make the mistake of mixing up the world of facts with the world of ethics. For instance, let us say that today's findings were overturned, and the evidence clearly showed that the differences between the races were huge. Would it then be alright to enact blanket discrimination against a particular race? Of course not. Ethical principles like equality of opportunity, equality before the law and human kindness don't require a scientist to discover them, and nor can any scientific finding invalidate them.