This chart displays the number of refugees to have fled their home countries, or countries of origin, for each year between 1990 and 2014 (inclusive). The home countries have been limited to the top twenty countries to have experienced the highest cumulative count of refugees in this time period. As evidenced in this figure, Afghanistan experienced the highest number of refugees almost every year -- it was recently eclipsed by Syria in 2014. The peak in Afghanistan's refugee count in the early 1990s can be attributed to the Afghan Civil War (1989-92). Afghanistan also saw an increase in refugees between 1999 and 2001, presumably as a result of Taliban activity and warfare (and ultimately, U.S. military involvement).
The data is provided by the World Bank, as a part of their World Development Indicators dataset (source). The World Bank compiled the data from several sources, including the U.N. High Commissioner for Refugees Statistical Yearbook and the U.N. Relief and Works Agency.