When Do You Have To Identify Yourself to German Police?
If a police officer stops you at random in the U.S. and asks to see your I.D., do you actually have to show it to them? Legally, no, barring extenuating circumstances. If a police officer in Germany stops you at random and asks to see your I.D., do you have to show them too?
Yes. Unequivocally yes.
The German authorities have the right to stop you and ask to see your I.D., which as a tourist in Germany would be your passport alone (or drivers license, if you are driving obviously). As someone who is living or studying over here, that means you're expected to show (at the barest minimum) your Aufenthaltserlaubis (your residence permit) and the green Zusatzblatt (the green slip that goes along with your permit card).
German police don't stop people left and right, but they are more likely to stop people around train stations, on trains with international connections, or areas like bus depots. Depending on the location, they are checking for the proper paperwork for being in Germany, or are working to discourage loitering.
If an officer stops you and asks for identification, you have to comply. If you don't speak enough German to actually converse with them, say so ("Ich kann kein Deutsch"; "I can't speak German"). Often, either they, or one of the officers with them, can speak enough English to clarify what they need; if not, they can call someone to assist you.