It is mandatory in Germany to at least have a liability insurance for your car. If you own a quite expensive car (partial) comprehensive insurance might be useful for you as well.
Fully comprehensive insurance: Depending on the car model, year and the annual mileage, the fully comprehensive insurance can vary greatly. The average price is €565 per year.
Partial comprehensive insurance: The price depends on your car and the chosen deductible amount. The average price is €340 per year.
Car liability insurance: The average price is €250.
Car liability insurance covers all damages you cause others with your own vehicle. E.g. if you cause an accident the damages to the other car are covered. (Partial) comprehensive insurance also covers damages caused to your own car by yourself or (in most cases) also by unknown third parties. You can insure your car e.g. against damages from accidents, vandalism, weather and animals.