Below are the global yearly average results from the Hadley Center for Climate Change's version 3 model. This model assumes that we don't make major cuts in our emissions of CO2, and that the world economy grows as generally predicted over the next century (this is the 'is92a' scenario). Read more on these assumptions and scenarios here.
The model alarmingly shows the Amazon basin warming by over 5 degrees C (9 degrees F) and drying out substantially. This would wipe out the entire Amazon rainforest and replace it with savannah. There are other climate models, and not all show this result (this model has 'medium sensitivity', so it is not extreme). Indeed, predicting future climate is like trying to predict the what the weather will be like in a week. There is a lot of uncertainty. Nonetheless, this is a possibility. To see what the other general effects of the region, many of which are more certain, go to All Countries, or look at the individual country links above.

source: http://www.metoffice.com/research/hadleycentre/models/modeldata.html