A recent paper published in Proceedings of the National Academy of Sciences argues that a record drought in 2007 through 2010, combined with poor agricultural practices and environmental problems, led to "widespread crop failure and a mass migration of farming families to urban centers" at the same time, refugees from the war in Iraq were flooding into Syria as well.
This combination of events destabilized the country and, combined with the brutality of the Assad government, contributed to launching to devastating Syrian civil war in 2011.
The researchers attribute the existence of the drought to natural climate variations, but also cite evidence that it's unlikely that the drought would have been as severe had it not been for for the contributing factor of human-caused global warming.
Many articles on climate change talk about longer-term consequences, but the most immediate bad effects are damage to agriculture and the economy, leading to masses of human beings fleeing unsustainable regions of the war and provoking all manner of problems including wars.
A brief abstract and a link to the full article can be found on the journal's websitehere. For a nontechnical discussion see this National Geographic article. You might also be interested in another National Geographic piece from mid-2013 that examines other forecasts of violence resulting from global warming.