One study I saw a while ago predicted that most languages would die out over time, leaving English, Spanish and Mandarin.

Language is a lot like evolution. It evolves over time. English 500 years ago was very different to the English of today. Thousands of years ago as populations moved and became more isolated, new languages evolved, which is why English has elements of Latin, French, Italian and Scandinavian languages.

Ironically, with greater communication, I suspect the opposite will be true into the future. As we start to communicate globally, languages will start to mix and become more similar as we start to use more and more 'foreign' words in each others languages as we understand each other better.

So I reckon that in 500 years, English will haver changed a lot, but will still be mostly recognisable with lots of new technical terms and a good spattering of German and Asian words coming into common usage.

Latin is not dead, its just that the dialects of latin don't understand each other anymore, (and they hate each other) so they became different languages.
English probably will change a lot, but due to wide acceptance as lingua franca and the rise of India as a power even in case of US loosing its hegemony, some kind of english will continue to be spoken and the exchange of cultural products will keep it more or less coherent. But of course, US and UK will loose gradually the control over the accepted dialects.