Very good answers so far. A photocopy will do the trick, perhaps even a DL but I'd go with a photocopy of the passport. Besides that the chances of you being mugged or robbed in Germany are very slim. Crime rates (especially violent crimes and gun crimes) are way lower than in the USA.

Police is most likely not going to stop you at any point during your travel, unless, as previously and correctly stated, you are in a car accident or something like that.

Every German is required starting at age 16 to carry a personal ID (not a passport). Theoretically they can stop you any time and run your ID. If they don't find anything they MUST let you go. You will find several things, cops are less martial looking, less power-trippy and better educated/trained in Germany. After that, they are still cops.

I have never ever been stopped and asked for an ID in Germany, not once. I have seen them stop and id people who are not white (yes, we got racial profiling, too) to fight illegal immigration. I have also seen them stop and id punks or skinheads, the former for drug checks and to make sure the mayor's son wasn't loose again, the latter to fight right-wing (nazi-like) organizations.

So no big deal.