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There are typically four kinds of rental insurance:
CDW (Collision Damage Waiver) / LDW (Loss Damage Waiver) is the most important insurance to buy. This covers accidents, theft and the associated lost revenue in charges.
Liability coverage - this covers you from legal liability in case of a lawsuit.
PAI (Personal Accident Insurance) - this covers your medical expenses in-case you are in an accident.
Personal Effects Coverage - this protects your belongings in the car.
If you are a foreigner - then its likely any protections you may enjoy under your normal car and health insurance do not apply overseas when renting cars; so you must have the CDW and the liability coverage.
If you already have state-mandated car insurance, it comes with liability coverage - as long as you are licensed for the vehicle type/class. So you can exempt yourself from that.
Your medical/home insurance may also cover you in case of rentals - but again, this only applies if you have medical insurance for the country where you are renting the car.
Finally, your credit card probably offers car rental insurance (most do). However, keep in mind to avail it you have to rent the car on the card and decline or accept the minimum CDW from the rental agency - check with your card policy on the specifics.