It may seem common sense to some, but self insuring is a risky proposition. Let's say you decide to go with the minimum legal auto insurance coverage of 15/30/5 in California (and similar low requirements in many states). Those are the minimums and refer to what and how much will be covered for liability, bodily injury and property damage. These limits are far too low to cover many accidents.
The "5" in 15/30/5, refers to the amount of property damage coverage you have for vehicles or items you are responsible for repairing, should you be liable for an accident -- this amount is $5,000. How many $30,000 cars are on the road? Well....many! This means, of couse, that if you cause the accident that causes more than $5,000, you are responsible for paying the difference. Effectively, that's like having another deductible to pay - one that is perhaps three times your coverage!
Unless you have that money in your bank account, the courts may decide to go after other assets if you aren't liquid enough to satisfy the judgement that will come your way. The other part of the state required amount of coverage, the 15/30 part, refers to bodily injury -- $15,000 per person, $30,000 per accident. Long story short, if you put someone in the hospital, with emergency room visits, xrays, scans (not to mention setting a break, or physical therapy), can easily drive the cost for one injured person over $150,000, if not $300,000. Average settlements for injury cases are in the hundreds of thousands of dollars today, not tens of thousands like decades ago.
Would it be a simple thing for you to come up with the difference on an injury claim? If taken to court, a trial and attorney costs can eat into your life savings and then some. In a serious accident the attorneys on the other side are going to investigate how many and what kind of assets you have and pursue that amount. If you have $500,000 to your name, that's what they want. If you have more, they'll be going after more.
Depending on the insurer you go with, substantial increases in liability can be increased with relatively low increase in your premium. It's like buying a decent refrigerator. A good one will take care of you for a long time. Get a bad policy or one that minimally covers your assets (not just your car) and you'll be paying for more than the food that's going to spoil in the fridge.
Don't you want a policy that's going to serve you well and pay when it's really important that it does so? It's a good way to go. The best way, frankly. It's only then that you can drive with the ease of knowing you are covered for almost anything, anytime, and have no worries. And the best thing? It costs you next to nothing to do it right.