If you are not independently wealthy, then you should carry Renters Insurance.
True or False? Your landlord is responsible for any damage to your personal belongings?
False - All you need to do is look in the paper on any given day and you will see that crimes have been committed and catastrophes like fire and floods that have taken place... nobody is exempt. Accidents happen, they happen all the time. Nobody plans them, that's why they are called accidents.
The owner carries insurance to protect his property, the real estate. If a water pipe bursts, it isn't going to be the owners responsibility to replace your personal items. Every year we have tenants lose their belongings because something happens.... GET INSURANCE!