The Tower of Babel
Adam and Eve got tossed out of Eden for their sin. Cain was cursed by God for murdering his brother. The whole world - except Noah and a few members of his family - were drowned in the Great Flood. But a few generations later, mankind was at it again! To rebel against God they decided to become united and build a tower to show man's glory.
Then they said, "Come, let us build ourselves a city, with a tower that reaches to the heavens, so that we may make a name for ourselves and not be scattered over the face of the whole earth."
Like a lot of events in the Bible, a casual glance at this statement suggests no evil intent. On the contrary, the plan seems to be to unite all people with a goal to reach heaven, a true ecumenical dream! But look more closely, and you can see the hand of Satan at work. God had explicitly told Noah: "Be fruitful and increase in number and fill the earth." (Genesis 9:1) And yet, here was man saying: "Let us make a name for ourselves and not be scattered over the face of the whole earth."
However, God decided to stop their plans. At the time, everyone spoke the same language, but he caused the people to begin speaking different languages, and scattered them over the face of the earth.
So the LORD scattered them from there over all the earth, and they stopped building the city. That is why it was called Babel - because there the LORD confused the language of the whole world. From there the LORD scattered them over the face of the whole earth. (Genesis 11:8,9)
It is logical to assume that people who spoke the same language would band together, and to prevent discord with other groups would move away and settle down independently. This seems to be the Biblical explanation for where the different races came from!