Anyone who has bought a house is obliged to take out opstalverzekering (residential premises insurance). This is a condition to get a mortgage. If you have bought an apartment, your Vereniging van Eigenaren – VvE (homeowners association) should provide the insurance. Otherwise, you have to arrange this insurance yourself.
A popular insurance in the Netherlands is the so-called inboedelverzekering (household contents insurance), which covers damage to your household goods caused by fire, burglary, explosion, storms, water, and various other factors. The sum insured will usually be subject to the average value of the contents in a house, so it is important that the sum insured is up-to-date.
The owners of furnished rented properties usually pay the residential premises insurance for expats renting a house or apartment. Check this with the owner.