Certain types of insurances such as health, accident, vehicle and home (if you are a homeowner) are compulsory in Switzerland, while there are several other useful ones such as  household contents and 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 about accident insurance as you will usually be covered by the company's policy. 
In our Local Guide/ Insurance section, you will find a choice of companies which can provide you with quotations based on your requirements. Premiums can vary greatly so it is always worthwhile comparing quotations.