Upvote:4
Close to the German-Swiss border, there are plenty of those services (Google for "lieferadresse deutschland"). They are designed for Swiss customers who order stuff in the EU and can have it delivered to a EU-adress, which is faster and cheaper. You usually get an email when something has arrived, and you pay a few euros per parcel/letter.
In Berlin, without any non-EU country in the vicinity, there aren't that many. I found one here and also here - no prices given unfortunately.
Upvote:9
For letters (but not always parcels), you can also use general delivery. In Germany, it's called βPostlagerndβ.
You don't need to do any paperwork beforehand but you need to check that a given post office offers this service and find the correct postal code using this website. You will then have the person sending you mail use the following address:
[Your name]
Postlagernd
[Postal Code] [City]
Letters from Germany are kept for 14 days, letters from abroad for one month.