Believe it or not, there is sound in space. It’s just not the type of sound we’re used to. The sound waves we normally listen to are mechanical waves, which means that they require a medium to pass through (i.e. air). Space is virtually a vacuum, which is why you wouldn’t hear anything if you stuck your head out of a spaceship.
Electromagnetic waves, on the other hand, can travel through the vacuum of space. The interactions between certain particles results in vibrations that produce electromagnetic waves. With the proper equipment, one can “record” these vibrations. Spend a little time converting those recordings into audio format and voilà! You can “listen” to those recordings. Various satellites and probes, such as SOHO and the Voyager, have done exactly that. For example, here’s SOHO’s recording of our Sun (skip towards the end, near 1:41 or so):
Want to hear our planet? This is Earth:
And, finally, here’s Saturn composing the soundtrack to your nightmares:
The descriptions of those videos do a decent job explaining how those sounds are being generated, so if my brief introduction didn’t satisfy you, I hope the words of others, who have taken the time to find and make these astonishing works available to the public, does.