A comment brought up the UNEP and United Nations University 2005 forecast that 50 million people could become environmental refugees by 2010.
I've never actually seen the real number, and the commenter didn't give one, but 50 million certainly seems likely to have been a vast overstatement.
But the actual science has been quite good. Consider this: the IPCC's First Assessment Report (1990) includes projections of sea level rise for the period 1985-2030 (Ch9 Table 9.10 pg 276):
(This looks like a digital scan of the all the original, and apparently the decimal points didn't cut it.)
How does this compare to reality? Well, it's not 2030 yet, but Aviso data on sea level show an average rate of (linear) change for the 22.8 years of their data (1993.00 to 10/25/15) is 3.34 mm/yr. So for the 45 years considered in the FAR above, that works out to a projection (if linear) of 15.0 cm.
Compare to their "best estimate" of 18.3 cm. Pretty damn good, especially when you consider that the scientific projections, which aren't linear as they include sea level rise acceleration, will likely be more than my number, so closer to the "Best Estimate" above, if not beyond it.
It's undoubtably very difficult to project what people will do in response to specific aspects of climate change -- there aren't many laws or equations in sociology. The UNEP and UNU were probably reckless in making such a projection, even over a short time period. It would be interesting to understand how they were so wrong, and der Spiegel does some of that here.
But the science here looks quite impressive.