There are several kinds of insurance in Germany. We are going to mention three of them that we consider really useful, it is optional to have them but they can avoid a lot of headaches.
The “Privathaftpflichtversicherung” is a form of liability insurance. The special function of it, is that the private person that is covered and her/his family will be covered for any type of unintentionally caused damage they might cause. The liability insurance covers all the typical risks of everyday life. You might hit a window unintentionally, your kid might stumble over some box full of porcelain that your neighbour left in the staircase, etc.
The Hausratsversicherung is an insurance that covers for any kind of damage that can occur to a rented or an owned flat. This means, it especially covers fire, water, storm or burglary damage. Usually, it also covers the cleaning costs after such a damage. If you use a computer or other items, they will also all be covered by it.
The legal expenses insurance (Rechtsschutzversicherung) covers all costs that a legal conflict might cause. It will cover lawyer costs, as well as the costs for the whole process, in case that it needs to be paid. It is common that one is covered up to the amount of 250.000 Euro. This insurance also covers the legal partner and kids. You can find many different providers for insurance, all with similar prices. We would recommend you to try and get all insurance covered by one same provider. This makes things a lot easier.