More than 60 samples have been added to the agency's new dedicated Soundcloud account, but listeners are unable to leave comments underneath the files.
Astronaut communications, including "Houston, we've had a problem" and "the Eagle has landed", can be heard - as well as some more abstract noises made by working spacecraft and debris.
In space itself, sound is unable to travel as there is no air.
"You can hear the roar of a space shuttle launch or Neil Armstrong's "one small step for [a] man, one giant leap for mankind" every time you get a phone call, if you make our sounds your ringtone," the space agency said.
"Or, you can hear the memorable words 'Houston, we've had a problem,' every time you make an error on your computer."
The sound library goes alongside Nasa's extensive picture library, which is also available free.
The space agency launched its account at the same time as Twitter enabled users to embed audio into tweets.