Some insurances such as Health, Accident, Car, Motorcycle, Bike and Home Insurance (if you are a homeowner), are mandatory in Switzerland. There are several other useful ones which are good to have such as Household/Liability and Legal Insurance.

In order to live in Switzerland, you must show proof of coverage by a Swiss Health Insurance company.  You have the choice between compulsory insurance with basic coverage or complementary insurance with additional coverage.
Ask your employer for the Accident Insurance - usually you will be covered by the company's policy. 

In our City Guide/ Insurance (coming soon) section, you will find a choice of companies who can provide you with a quote according to your needs.  It's worth comparing, as the differences in the cover on offer can be substantial.