Do I need to have private liability insurance?
It is not mandatory, but you might consider getting a third-party private liability insurance (Haftpflichtversicherung). It will cover you or any insured member of your family in the event that you commit an act for which a German court would consider you ordinarily negligent.
Under German law, there is no limit on the level of damages an individual could have held against them for an act they have committed—even an unintentional or innocent act resulting from carelessness.
Ordinary negligence could be a simple matter of damaging someone else's property, for instance knocking over a vase in a shop, causing an accident as a pedestrian by not crossing at the pedestrian crossing, or causing bodily injury whilst skiing or engaging in other sports activities. This essential insurance is intended to give you more than just peace of mind, and is strongly recommended and often contractually required when you lease property.
Any damage claims can be distressing, and a high level of coverage (we suggest ten million euros for a family) costs relatively little (around 20 euros for a family, 10 euros for a single person).