A word of warning:

On a recent trip I bought a SIM card from Edeka mobil (at a supermarket near my hotel). It turns out that this particular provider cannot and will not allow you to register if you are not resident in Germany!

Their customer service is horrible! It took several days for them to respond, and it then took several back and forth emails with them until they finally told me I could not use their service.

The store itself was very reluctant to take back the SIM card as the package had been opened, but finally did so when presented with a printout of the email I had received.

Overall, this was a very frustrating experience!