'Serenity to ISS on STS-117'
At 7:38 PM Eastern time on June 8, 2007 - the shuttle Atlantis lifted off from the Kennedy Space Center on its way to the International Space Station. An astronaut, Mission Specialist Steven R. Swanson, aboard the shuttle mission was carrying DVDs of Firefly and Serenity to add to the station's movie collection.
That's the short version.
The Breaking Atmo website contains a chronological history of how this came about, from the transmission of Captain Malcolm Reynold's speech about 'love' to the crewmembers on the ISS, to the final launch of the mission. The site also contains links to relevant NASA pages.