There indeed are different races, espacially in medical science that is becoming more and more important.
There aren't, there are different groups among us that share common traits, but that's it. E.g sickle cell anaemia...... it's a genetic condition that natural selection has actually encouraged. It's common in populations that inhabit malarial problem areas. sickle cell is horrendous, if carriers have children then out of four kids one will die, two will carry the trait (and have sickle cell crisis) and one will be fine.
Normally natural selection will ensure the bad genes are lost, but in this case the healthy kid will probably get malaria and die... so the sickle sell carriers are actually the ones that survive (sickle cell trait protects against malaria).
Now most sickle cell carriers/sufferers are black, is it something only that 'race' can get? Nope, anyone can inherit it, it's just that the population who had it were concentrated in Africa, where most people were black. Simple as that. If a black carrier/white couple have a kid he/she can inherit it. If that kid has children with a white person, their offspring could be a carrier..... in two generations a child is born who's white and carries sickle cell. (one black grandparent, usually ends up apparently white as 'race' specific cosmetic characteristics are lost).
So, medically, there are no races, geographically and sociologically there are. If you think otherwise, name a disease/condition that can only be caught by a member of a certain race and could never appear in a different group.
If a white man moves to Japan, then within a couple of generations his familly will appear to all intents and purposes Japanese. So how the hell could we be of different 'races' our DNA is 100% compatible, there are no characteristics that are totally unique to one race and can't appear in the others.
It's no different to dogs, biologically a dog is a dog. we then bred them into a variety of different shapes and sizes, but they are all still dogs. Our differences are caused by geographical barriers. We picked up traits suitable to where we lived, so we condensed those differences. Now that we can fly anywhere in the world these differences are being watered down.