In Germany, anyone who causes damages to another party can be held liable. Parents are liable for their children. It is therefore customary to take out a private (family) liability insurance policy to insure against any claims that may arise from unintentionally caused damages.
Liability insurance should at least cover all private liability claims, and as much business-related liability claims as possible.
If you are funded by a scholarship, check whether you have liability insurance through your scholarship provider.
Motor vehicle owners in Germany are required by law to carry motor vehicle liability insurance.
For animal owners (especially dog owners), it makes sense to purchase a liability insurance policy for animal owners.