Documentation, Insurance and Administrative Obligations
Every vehicle on the road needs registration (Zulassungsbescheinigung), liability insurance (Haftpflicht) and, where due, a valid inspection (Begutachtung, usually every year for older vehicles and every two years for new ones in the first years). Carry the registration and insurance proof; the licence must be carried when driving. Liability insurance is mandatory and covers damage you cause to others; comprehensive (Kasko) is optional and covers your own vehicle.
Administrative duties: report changes of address or ownership, return plates when the vehicle is deregistered, pay motor-related taxes (e.g. motor insurance tax, fuel tax via fuel) and the motorway vignette for motorways and expressways. Know the inspection sticker and the emissions rules. After an accident, you must give your details and inform your insurer.
Traps: assuming liability insurance covers your own car (it does not); driving without a valid inspection (it can void cover and bring penalties); forgetting the vignette on a motorway.
Worked rule of thumb: before a long trip, check four documents: licence, registration, insurance proof, and vignette/inspection validity. Missing any one can mean fines, and a missing vignette means the full day's replacement fee.