You may want to Google rental car accident fees to get an in-depth knowledge of the topic.
Generally, there are four charges if in an accident:
Damage to car/theft: this is covered by the Loss & Damage waiver sold by the car companies, your personal insurance, and by some credit cards/corporate contracts. Your exposure is determined on who is primary (your insurance, the credit card, etc) and who is secondary. It is best to have a card/contract as primary, or your insurance will be billed; however, most credit cards require the renter to decline the LDW from the agency in order to be in effect. Thus, you can't usually get coverage from both Visa and
Alamo to "double up". In addition, there are some limitations by credit cards on auto theft, though.
Personal injury (aka Liability): if the accident is your fault (or if you are hit by an uninsured driver) and someone is hurt, separate insurance is needed. Usually, this is covered by your personal auto policy. if you don't have liability (or insufficient for the State you are in), you may be very exposed. Some credit cards will have a liability component in addition to comprehensive coverage. You can usually purchase coverage from the rental agency. Be sure you have enough insurance here, as medical bills can be expensive.
Loss of Use: Car rental companies will charge the renter if their vehicle is "taken out of service" for repairs to make up for the lost revenue. Some credit cards will cover this (in theory), but in reality a pissing match ensues where the credit company requires proof from the rental company as to the real estimated usage of the vehicle, while the rental agency doesn't want to provide it as privileged info. Thus, the renter ends up picking up this tab. In addition, the amount is based on "rack rate" instead of the discounted rate generally offered. This gap may be hard to fill.
Administration fees: Almost all rental agencies charge administration fees to process the damage claim and insurance info. Reports indicate this could be a couple thousand dollars, depending on several variables. Ask your auto insurer for their recommendation about this.
Personally, I have USAA and use their car rental codes, instead of the super low coupon, to ensure coverage of all four. In addition, AMEX has a car rental insurance policy that card holders can buy ($25) that makes them primary (instead of secondary) for damage to the car (comprehensive/collision) and liability (damage to people) that is pretty good. A such, I have doubled (and in some areas tripled) up. Look at different combinations to get the best coverage for you.
Good luck!