I must have heard about the shortwave numbers stations years ago on this Lost and Found Sound recording for NPR's All Things Considered (original page, YouTube version).
The story was strange, the recorded sounds spooky, and the low-fidelity of the shortwave signal making them sound even spookier, as if other sounds and voices are edging their way into the transmissions. (I guess in this context, "spooky" has more than one meaning.)
It seemed -- and still seems -- so weird that in this day and age, when so much of the world is gridded and mapped and monitored that there are still spy organizations (for lack of a more correct term) out there doing this: playing a tune or song to alert whoever is receiving the transmission and then reciting a series of numbers, letters, or words. We don't know who is sending the transmission, who is receiving it, or what the numbers mean.
And this is happening everywhere, it seems, not just the old Cold War countries. When I listen to the recordings of these stations, I feel an eerie tingle creeping up the back of my neck. There is still mystery in the world, still things that do not want to be known. I read somewhere that the best way to listen to these recordings is late at night, with the lights off. That sounds right.
The Conect Project has 5 CDs worth of these recordings collected from all over the world and over a long period of time. The first four CDs worth of recordings -- collected over 20 years through 1997 -- can be heard and downloaded for free via archive.org. Also free is the 80-page CD booklet in PDF, describing the project, the shortwave stations, and every track. You can also download the free sound files and PDF or order the CDs from Conet's official site (which offers links to other sites on the numbers mystery).
The first four CDs are available as a digital file from Audible.com (for the exceedingly odd price of $2.09) or from Audible's parent company Amazon for only 95 cents! Inexplicable.
Other resources: Wikipedia links to The Conet Project and Numbers stations, and the results of a Google search on "the shortwave numbers mystery."