A few years ago, a friend of mine had an interest in shortwave radios and as well as the guilty pleasure of eavesdropping on the local law-enforcement agencies, I was also much amused to discover the existance of so-called 'number stations'. On these stations one could listen to mechanical-sounding voices reciting numbers interminably. My friend explained that these were secret coded transmissions to spies, though I took this explanation with a grain of salt.
Needless to say, activities of this sort attract attention on the internet and this page by Simon Mason gives a good introduction.
Also, if you scroll down to the bottom of this page you'll see that there are recordings of various number stations for you to listen to.
Amongst my favorites are:
The Lincolnshire Poacher, seemingly operated by the British Royal Air Force. It is so-called after the cheery ditty used as a call-sign
The Stasi Gong Station
Sweedish Rhapsody, a Polish broadcast with a music-box intro
Papa November, a West German broadcast
This page of miscellananeous stations, including a Spanish broadcast using 'Don't Cry for me Argentina' as a call sign.
On a slightly related note, it used to be the practice of the Secretariat of State to broadcast messages to its Nunciatures on the Vatican Radio frequencies.