When you rent a car a basic insurance is often included. In my opinion this basic insurance is insufficient because it offers only a limited coverage of damage. Also an own risk is often applicable. Because every country has its own legislation the exact coverage depends on the state where you renting/driving. Rental companies will offer additional insurances.
LDW (Loss Damage Waiver) or CDW (Collision Damage Waiver)
A LDW or CDW insurance takes care of your own risc. When for instance your rental car gets stolen or damaged then the LDW will cover the costs. When you rent a car via a travel agent in your home country LDW/CDW is often included in the rental fee. I strongly recommend that you take this insurance.
LIS (Liabillity Insurance Supplement)
A LIS is often not included but is recommended. LIS covers you for the costs of any damage or injuries that are a result of an accident you are involved in. A LIS insurance will cost about USD 6-8 per day.
Other types of insurances
Other insurances are PAI (Personal Accident Insurance), UMP (Un- and Under insured Motorist Protection)
Insurance is expensive so check if you really need to accept any type of insurance. Your rental car may be covered by your car insurance, your travel insurance or any other insurance you have. Also credit card company sometimes include a rental car insurance if you pay with that credit card.
Anyway you should make sure that you are not under insured. Otherwise If you are involved in an accident you might end up paying for any damages.