My colleague burst out laughing when he saw the letter, and explained it to me.
It turns out that everyone in Germany who has a radio or a television has to pay a fee to use them.
If you have a TV you have to pay 17 Euros every few months, and if you have a radio you pay 5. It doesn't even matter if you never use said radio or TV – if you have a device (even a computer) that can access TV or radio, you have to pay these fees. If they catch you with a TV or radio and you haven't paid you can be fined up to 1,000 Euros. Of course, there's no real way for the authorities to actually go into your home and check if you have a TV or radio, so they resort to sending scary letters.
I have no TV, no computer... but I do have a little radio, so I guess I'd better start paying up.