Car insurance is for idiots. And the poor. Much as the smiling Gecko and the cartoon lady superspy mascots would have you believe, car insurance is an absolute ripoff. Unless you are in dire financial straits, buying any more than the absolute minimal insurance required by law is a waste of money.
Any insurance company works by balancing risk (expected payments to you for car damage) with reward (your monthly premiums). So by calculating your risk and cost of an accident from various demographic factors (gender, age, the car you drive, past driving record, location, etc.), insurance companies arrive at the estimated cost of car damage per year, tack on a fat extra commission for themselves and call it your yearly premium. This means that for whatever insurance option you choose, no matter what the deductible, car insurance companies expect to make money off of you. And they do! Auto insurance companies post billions in profits every year out of your pocket. No matter what the great "savings" you get by switching providers might be, most people will lose money.
It's much like playing in a sort of sadistic casino, a strange risk-adverse one. You can either choose to bet (pay a premium) every month to avoid an improbable yet very costly loss (repairs for an accident). The house (an insurance company) much like every other casino, "always wins"- the odds are stacked in their favor for them to take home big profits, you included.
Now, taking such a gamble could make sense, depending on what you have to lose. However, you're expending hundreds, possibly thousands of dollars per year on maintaining a CAR, not your life (health insurance). A car, for most of us, is simply a luxury item. We are entirely capable, though a tad inconvenienced by the absence of a car and can get along driving a dented or damaged vehicle just fine. Only if you have limited funds for a repair, your livelihood or your ability to reach your workplace depends on you having a car and you would have no other way of getting to work in the event of your car being totaled should you consider anything more than the minimum.
The auto insurance industry will play boogie-man with you, giving scary statistics as to the percent of drivers involved in car accidents every year. In reality, most car accidents are minor scrape,bumps and dents which deal only cosmetic damage to a car and do not actually impede it's ability to get you from point A to point B. The probability that you have an expensive accident which actually prevents the car from running is very, very small.
My advice? Ditch all but the minimum liability insurance required by your state. Raise your deductible as high as any company will allow you to. Invest the money you would have spent on insurance premiums. In the long run, you will very likely save and earn a ton of money. If your car gets hit, guess what, pay for the repairs yourself out of what you've saved. If you can't pay for the damage, chances are you can still run your dinged-up car without any intervention at the shop.