I recently visited what is apparently a prepaid-SIM-without-ID island of the Czech Republic, accustomed to places where registration is required. The person in the telecom store selling me the SIM looked at me with an almost disarming "this is the Czech Republic" look when I asked if she needed to see my passport.

In Germany you now apparently need to show ID and provide an address, though no proof of residence so any address seems acceptable.

In Germany, I need to do PostIdent or handover my address+copy of my ID/passport to buy a SIM card. To further check things, telecom sends letters to corresponding address too sometimes.