Blue Gemini was the designation of a US Air Force program intended to develop a military space craft based on NASA's highly successful Gemini capsule. The idea for the program was first introduced during February of 1962 at Congressional hearings on the US defense budget. Blue Gemini was intended to be the first part of an ambitious 10-year program to build a military space program in the United States. The associated alphabet soup of acronyms and codenames soon followed -- Blue Gemini quickly became the jurisdiction of the Air Force Space Systems Division (AFSSD), where it fell under the umbrella of the Manned Orbital Development System (MODS) program, a larger effort to build USAF space stations (called MOLs, for Manned Orbiting Laboratory) which would utilize Blue Gemini craft as ferry vehicles.
By August of 1962 Blue Gemini had become a much more coherent program, with immediate plans for 6 Gemini missions with Air Force pilots. These missions would act as training and orientation missions for the Blue Gemini and MOL crews. Despite initial enthusiasm on the part of certain Air Force officials, as well as within NASA, the program had many detractors, among them Curtis E. LeMay, then the Air Force Chief of Staff. These August 1962 plans are the closest Blue Gemini ever came to fruition.
In late 1962 a series of meetings was set up between Air Force and NASA officials to lay the groundwork for the 6 planned Blue Gemini missions, which were to be cooperative between NASA and the USAF. It was at one of these meetings that Secretary of Defense Robert McNamara proposed that NASA's Gemini program be merged with the USAF Blue Gemini project, and that the new, combined effort be moved to the jurisdiction of the Department of Defense.
In the early months of 1963, Blue Gemini essentially petered out. McNamara lobbied heavily for as much as $100 million in defense spending on the program; however, many at NASA -- and even within the Air Force itself -- disliked the implications of a military space program. The implications of such a takeover were uncertain; many questioned whether the military would expect a similar level of cooperation on the upcoming Apollo program, and some even voiced concerns that such cooperation would threaten efforts to reach the moon ahead of the Soviets.
Also threatening the future of any military space program was the fact that the mission of such a program was unclear at best. The first MOLs, which were being planned concurrent to Blue Gemini, were intended to be orbiting observation posts, where USAF astronauts could monitor Soviet military activity. At the same time, the first generations of spy satellites were beginning to show the potential of unmanned observatories. If the MOL were shown to be unnecessary, Blue Gemini craft would have no where to go.
Blue Gemini would continue to exist in one form or another until the end of NASA's Gemini series in November of 1966, but the Air Force program would never make it out of the planning stage; in the end, there was no way to justify the expense of such a program and the associated risk of human life. The only lasting impact of Blue Gemini was the Gemini Project Planning Board, an advisory commitee which was confined to planning for military experiments to be carried out on NASA Gemini capsules, by NASA astronauts. Gemini's younger, more militaristic sibling was relegated to the dustbin of history, and the United States has yet to field an (official) military space craft of any sort.
For much of Blue Gemini's short life, it was in competition for funding with the Air Force's home grown military space craft, the X-20 or "Dyna-Soar." The two programs competed with one another until December 10, 1963, when the X-20 was officially canceled and funding from that program transfered to the MOL. For information on the Dyna-Soar spacecraft, see orac's excellent writeup here.