The topic of the tower of Babel came up in comments so I wanted to comment on it further. There are some references in chapter 10 that speak of multiple languages, before the story of the tower of Babel.
Descendants of Japheth
Genesis 10:5 From these the maritime peoples spread out into their territories by their clans within their own nations, each with its own language.
Descendants of Ham
Genesis 10:20 These are the sons of Ham by their clans and languages, in their territories and nations.
Descendants of Shem
Genesis 10:31 These are the sons of Shem by their clans and languages, in their territories and nations.
The Genesis writer took the time to explain that the descendants of Noah's sons all had different languages. It is unclear precisely when the story of the tower of Babel is set. Obviously in the same era. But there is nothing indicating that the table of nations in chapter ten comes after the tower of Babel. Genesis up until this point comes in a roughly chronological order (i.e each major story happens after the previous- Creation, Adam and Eve, Cain and Abel, Noah etc.)
Genesis 11:1 says that the whole world had a common language and speech, however it does not necessarily mean that every individual spoke this tongue- although they may have. We need to escape our monolingual world view, and imagine that the people at the tower of Babel already spoke more than one language. I.e they spoke the common language and they spoke their own clan's language.
My proposed (yet unprovable I know) hypothesis is that the common language was confused at Babel and then people could only use their clan's language after that point. Following this there was far less incentive to have a common capital in the world, and so the clans went their own way.
To me this indicates that multiple languages is a good thing. We often look at the tower of Babel as evidence that many languages is a bad thing. I don't see the result of Babel as a curse. It was discipline but not a curse. In each of the earlier stories involving people in Genesis, God gave out a punishment which was then immediately followed by Grace. So, I see that God was showing grace to the nations by forcing them into a place where they forged their own identity. The tower of Babel was dangerous because it was a clear possibility for outright control by a human being over the human race, which would make it harder for people to reach God. God removed this barrier when he destroyed the tower project.