How many countries have sent astronauts or other trained personnel to the International Space Station?
Wikipedia has a list of International Space Station crew where you can also find relevant statistics. As of January 2017, 10 nations have sent crew to the ISS: United States, Russia, Japan, Italy, Canada, Germany, France, Belgium, Netherlands and the United Kingdom.
However, more people/nations have visited the ISS: List of International Space Station visitors. This adds another 8 nations to the list: Sweden, Brazil, Denmark, Kazakhstan, Malaysia, South Africa, South Korea and Spain.
So in total, people from 18 nations have been to the ISS as of January 2017.