It may take you some time, as there are also various podcasts and jingles included, but if you dig deep enough, you might as well find the famous "Houston, we have a problem" transmission or Neil Armstrong's words "One small step for (a) man, one giant leap for mankind", as well as a lot of way more obscure, otherworldly sounds that literally came from the deep space. 

And if you're now wondering about clearing all those juicy samples you'll find, fear no more, as here comes the best part - it's all royalty free! However, the Creative Commons license it falls under requires proper attribution, but I believe that a little sample here and there will do NASA no harm. After all, my tune "Heartbeat", where one of Kennedy's speeches from NASA's Soundcloud is used, is still up there on all the stores and streaming services, standing strong ^^