Christian Aid, a UK charity, has issued a report that claims that climate change may displace as many as a billion people by the middle of the century. That would more than quintuple the current number of refugees worldwide. The report emphasizes the important point that most of those climate refugees will not be transnational migrants, but will be displaced within their own countries (IDPs, in the U.N. jargon). Most of the victims will be in South Asia, the Middle East, and the Sahel in Africa. Full report here.
A billion refugees strikes me as unlikely, but it's not beyond the realm of conception. What is unthinkable, on the other hand, are the humanitarian and political implications of such a crisis.