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.
Shannon Lucid
Shannon Matilda Wells Lucid (born January 14, 1943) is an American biochemist and a retired NASA astronaut. At one time, she held the record for the longest duration stay in space by an American, as well as by a woman. She has flown in space five times including a prolonged mission aboard the Mir space station in 1996; she is the only American woman to have served aboard Mir.