Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
International Space Station
Anousheh Ansari became the first Iranian in space and the first self-funded woman to fly to the station. Officials reported that her education and experience make her much more than a tourist, and her performance in training had been "excellent." Ansari herself dismisses the idea that she is a tourist. She did Russian and European studies involving medicine and microbiology during her 10-day stay. The documentary "Space Tourists" follows her journey to the station, where she fulfilled "an age-old dream of man: to leave our planet as a "normal person" and travel into outer space."