If you have any active auto insurance policy, they will request proof of it at the counter. Some areas are more strict than others depending on risk. Airports are less likely to ask for insurance info. However, you do not NEED auto insurance to rent a car because the company carries minimum financial responsibility for each car. If you do not take the coverage that they offer, and you do not have an active auto insurance policy, then you will be fully liable for all damages to the rental car. Generally, if you're domestic flying, they will send a legal team after you. If you are international, most rental car companies have Euro and Canadian branches to pursue damages.

Certain states are “no-fault” states. It doesn't matter whose fault the accident was, the renter is responsible for damages to the car if the additional coverage is not purchased. Some companies or local areas may allow you to pursue the at-fault person, but only with a police report and insurance/contact information of the at-fault person. If at-fault party and cannot pay, you are still responsible.

They also can send people to collections

If the car company you're renting from has out-of-state tags on their cars, they're probably self-insured.

Most rental car companies in airports deny debit cards, you need a credit card to rent. Some get away with a debit card if they have a return flight out of the same airport, but local policies may vary.

I will forever and always take the coverage for a rental car, and factor in a $ 25-a-day charge for it. I've seen too many headaches and hearts broken to not pay the extra. The last thing you want when you're traveling cross country with family is to deal with damages that were not caused by you to ruin your insurance/finances.