perfidy

Some of the things that NASA has resisted in the past forty years: 

Orion and NERVA 

Nucklear propulsion technologies that had successfully reached scale model tests for Orion, and static testing of a prototype for NERVA before being cancelled by NASA. The prototype NERVA (Nuclear Energy for Rocket Vehicle Applications) prototype was twice as efficient as the most advanced chemical rocket ever built, the SSME, or Space Shuttle Main Engine. With a little practice, this could have been improved. (BTW, my dad in his role as Air and Space Museum curator helped save the prototype, nicknamed kiwi.) 
Air Force Manned Orbiting Laboratory  

A small (mobile home-sized) space station that could have been launched in the mid sixties, and would have had a crew of two.

DynaSoar  

Short for dynamic soaring, the X-20 was the result of a different evolutionary line than the Apollo moon rockets. It evolved from the German Sanger-Bredt Silverbird intercontinental skip-glide rocket bomber from WWII, and was the first space vehicle ever actually constructed - back in the fifties. NASA cancelled it eight months before drop tests from a B-52 and a manned flight in '64. This spaceplane, launched atop a Titan II or other disposable rocket, would have led to a series of more advanced follow on vehicles. 

Skylab  

The Skylab program was cancelled by the ingenious expedient of having the space station fall from orbit on 11 July 1979. Although there were several proposals that might have saved America's first space station, the freeze on non shuttle launches left NASA with no means of getting there. 

NASP  

The National Aerospace Plane, a space plane that would take off and land horizontally, was unceremoniously cancelled in the early nineties. Granted, there were doubts whether the vehicle was feasible, and some research continues. 

DCX 

I've talked about this one before, on this site, though that week doesn't seem to be in the archive. 

NASA has also consistently resisted additional alternative methods of propulsion like solar sails and tethers, any use of Shuttle External Tanks other than throwing them into the Indian Ocean, going back to the moon for any reason, and any means of going to Mars that doesn't take fifteen years and sending Pittsburgh into orbit to supply the mission.