Should I purchase rental car insurance? What protection does my credit card provide?

Some roads in Hawaii are very narrow with a lot of rocks and other obstacles. Check https://duckduckgo.com/?q=hawaii+roads&iar=images&iax=1&ia=images
If you have plans to visit such places you might want to consider extra coverage.

From a comprehensive article posted on credit-land.com (emphasis mine):

So, credit card coverage includes damage and theft, but it does not cover personal injury, liability, or property. It also does not cover any driver who is not authorized on the car. Only the people named on the car rental agreement are covered. Also, certain types of vehicles aren’t covered – usually trucks, campers, and other specialty cars won’t be covered. Comparing with our side-by-side review of U.S. Car rental services, the only two items covered by any credit card rental insurance are LDW and CDW – car theft and damage. Supplementary coverage, personal coverage and medical coverage are not included in standard credit card rental car insurance agreements. SLI, PAI, and PEC are not included.

Credit card car rental insurance is always considered secondary coverage – it covers you if you don’t have other car insurance or if you do not purchase insurance from the rental company. A very important thing to know is that with any credit card rental insurance, buying the coverage from the rental company will invalidate your credit card insurance coverage. You can’t get coverage from both sources at once. However, if your personal car insurance has a deductible, then your credit card will cover that amount. Keep in mind, although your rented vehicle is protected, you will need a separate insurance to cover possible liability damages you may cause to the other vehicle or property involved in the accident. As always, the best solution is to be careful while driving.

There’s also a handy infographic on the site, not included here because it’s about 4 miles tall.

Coverage is specific to each policy which can vary greatly for each country so it is hard to generalise, but I’ll generalise anyway and hope it helps.

As you mentioned, there are broadly two types of insurance that you need to consider: collision – which covers damage to the vehicle; and liability – which covers damage you may inflict to others. Since insurance is a high margin area for car rental companies (at least in the US) it is smart to do your homework ahead of time and avoid making the decision at the counter

The first place to check is your own car insurance policy, if you have one. Generally it includes liability for any car that you drive and not just the car(s) that you own, so that which would include a rental car. It may also include collision coverage of rental cars depending on your policy which means that you do not need to purchase any coverage from the car rental company.

Some credit cards do include insurance for car rentals as a benefit, but this is specific to the particular credit card program. Call your credit card company to check the details of your coverage.

If you don’t have coverage through either of those, you can purchase third-party insurance which is likely to be cheaper than purchasing through the car rental company. Depending on the car rental company, you may on occasion need to provide proof of any external insurance coverage if you decline the rental company’s coverage. Also, in the case of damaging the vehicle, you may be required to pay the rental car company for the damage and then claim it back through your insurance provider.

You may also find rental companies selling personal belongings or similar protection. This is generally unnecessary as your belongings are likely covered by either your Homeowners, Contents, or Travel insurance.

As a side note — in my experience, insurance offered by the rental companies in the US is expensive (e.g. doubles the cost of the rental) but offers low or even zero deductibles. In Europe, the insurance offered by the rental companies is generally cheaper (e.g. a couple euros extra per day) but the deductible is much higher (e.g. €500-€1000) and they may require a deposit to cover it (e.g. a hold on a credit card). When I first rented a card in Europe I was shocked by this and wasn’t prepared to cover the deposit. But now I much prefer it as I no longer have a car insurance policy and hate paying the outrageous rates when traveling back to the US and there is no high deductible option.