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Everyone in the world had been speaking the same language, but of course that was just too dang convenient.
So these people thought, hey, ya know, we could just build this huge tower deal that would reach heaven and then we'd just be like the coolest people ever. God will be so proud of us. They should have known better. God was, in fact, not proud of the humans. The way he saw it was that if these humans could all understand each other, then there was nothing they couldn't do. So his solution to this was to diversify their one language into multiple languages and spread them throughout the world.
I don't really see this as a punishment from God. I believe that he thought that the humans would have no way to improve themselves if they were already perfect and and could do such things as build a tower to heaven. The language separation was a challenge that he set forth for the human race so that we could still have room for improvement as a species.

 Rather than learning a new language, I would like to study the history of languages in general. I find the development of languages throughout history to be fascinating. It's really intriguing how certain words can be morphed from language to language and how words can be shared and incorporated into other cultures.