It’s Against the Law
It's illegal to drive an uninsured vehicle in almost all states even if you don't have an accident. In some states, you can post a surety bond instead or place a significant cash deposit with the state that will pay for damages if things go south while you're driving. Some states allow you to file proof that you have sufficient assets on hand to cover the other guy if you get into a fender bender. But if you don't do any of these things, you're breaking the law, and having an accident can compound your troubles. You may be liable for stiff fines, and your license, registration or both may be suspended.
In no-fault insurance states, the other driver usually can't sue you for damages, even in you were responsible for the accident. He can only make a claim with his own insurance company unless his injuries are extremely serious and his medical bills exceed a certain threshold. The majority of states aren't no-fault, however. The other driver can sue you, and if you don't have insurance and he wins the case against you, you'll be held personally liable for his damages. If he gets a judgment against you, he can use it to place liens against your property or garnish your wages.Even if you file for bankruptcy, you can't get out of responsibility for paying personal injury debts if you were driving while intoxicated at the time of the accident.
Uninsured Motorist Coverage
Some motorists purchase special coverage to protect themselves against uninsured drivers. This type of coverage would kick in to pay for the other driver's damages to some extent if you caused the accident and carried no insurance on your own vehicle. It might reduce the chance that he'd want to sue you, particularly if you don't have a lot of assets and it's not likely that he could recover anything from you. But his insurance won't do you any good -- it typically covers only the insured's damages, not those of the uninsured driver.
Another potential pitfall might come about if you're driving perfectly responsibly and do nothing wrong, but the other guy runs a stop sign and broadsides you. Such an accident would clearly be his fault, but in some states, you can't collect damages for pain and suffering if you're not insured. You can only seek reimbursement from his insurer for your medical bills. This is called the "No Pay, No Play" rule, and a handful of states have adopted it. If you don't buy insurance for yourself, you can't seek pain and suffering damages from the insurer of someone who did purchase coverage.