In Germany and Austria for example the law clearly requires you to carry their local ID card if you are a resident, or your passport with your visa if you are a foreigner, or you can be arrested and fined.

However, in reality these Western European countries are not likely to haul you in and actually fine your or charge you with anything, but they do want to be able to establish your identity on the street so whilst technically unacceptable, in reality the suggestions others made are correct. Your local country's drivers licence and a photocopy of your passport should suffice.

In Germany I have often observed that the "Bundespolizei" do random checks in particularly around transport hubs such as central railway stations.

This has been justified as having to do with Schengen. The borders within Schengen are open, so in order to detect the odd illegal immigrant, checks within the country are necessary.