The flow of refugees is steadily increasing, according to the U.N. Refugee Agency (UNHCR). As of mid-2016, there were 16.5 million refugees globally, 5 million more than in mid-2013. More than 30 percent of all refugees as of mid-2016 came from Syria, the largest source of global refugees.If we look at total numbers you can see in the graph below that Turkey is currently hosting the greatest number of refugees--mostly from Syria. And, by the way, the U.S. State Department Humanitarian Information Unit has a nice infographic with more detail about Syrian refugees in Turkey.
The picture looks a little different if we consider refugees per capita. That puts Lebanon, rather than Turkey, on top.