For the other driver to be liable for the accident, and for his liability insurance to kick in, there must be evidence that he was negligent.

“Liability insurance is only going to pay if the injured party can prove the other driver is at fault in court or out of court,” says attorney Benjamin Zimmermann, a partner with Sugarman & Sugarman P.C. in Boston. “If you can't prove negligence, you can't win the case, and if you can't win the case, insurance companies know that and won't pay. One of the keys to a successful claim is to establish the other driver's fault early and thoroughly.”

The rules also vary by state, notes David Reischer, a New York attorney and co-founder of LegalAdvice.com.

In states with no-fault auto insurance systems, your own insurance generally pays for your medical bills, regardless of who was at fault, and you're restricted in when you can sue other drivers for injuries. However, in most no-fault states an at-fault driver may still be liable for property damage. It's a good idea to understand how the rules work where you live before you have an accident because insurance laws vary widely by state.

If you don't have collision coverage, which would pay for repairs to your car in an accident, you have to rely on the at-fault driver's insurance to pay for repairs.Here are five scenarios when the other driver's insurance company may refuse to pay out — even if you think it should.

1. The other driver has a sudden medical emergency.

“A sudden incapacitating medical event is a defense that is more common than people might think,” Zimmermann says.

If a driver is suddenly incapacitated by a medical emergency — a heart attack or stroke, for instance — he may not be liable if he didn't have sufficient warning before losing control of the car.

However, a driver could still be found negligent if he shouldn't have been driving with the medical condition or neglected to take care of his condition.

Attorney Thomas Simeone of Simeone & Miller LLP in Washington, D.C., says he represented a client whose car was hit by a vehicle driven by a pregnant woman who passed out behind the wheel. Simeone won the case because he was able to determine in court that the woman had enough time to pull to the side of the road safely after she started feeling flushed and before she fainted. Her insurance company then had to pay his client's claim.

2. You're hit by a fire truck racing to an emergency.

Anytime you file a claim against a government, “you have to jump through additional hoops,” Simeone says.

Local and state jurisdictions have varying rules and timelines for filing claims against them, and the standard for proving an emergency vehicle driver was liable is much higher than the standard for other drivers.

Generally if the siren and flashing lights were on, then you'd have to show gross negligence on the driver's part, not just negligence, Simeone says.

“A lot of lawyers don't take those cases,” he adds.

3. The other driver hits you because of an accident with a hit-and-run driver.

Depending on the state, you may be able to make a claim under your own uninsured motorist coverage, Reischer says. Uninsured motorist coverage covers your injuries if an uninsured driver, or in some states a driver who flees the scene, causes an accident.

Or imagine this scenario: A mattress falls off a pickup truck, causing another driver to crash into you, and the pickup driver manages to escape without anyone getting the license number. Your uninsured motorist insurance could come into play in this example as well, Reischer says.

Keep in mind that your word about a vanishing vehicle is not sufficient. You'll need evidence, such as eyewitness testimony, vehicle damage and a police report to back up the claim.

4. A thief driving a stolen vehicle hits you.

Generally an auto insurance policy covers you and other licensed drivers in the household who are listed on the policy and anyone you give occasional permission to use the car.

“When a thief takes a car, there's no permission or consent,” Simeone says.

So the car owner's insurance wouldn't pay. The thief's insurance, if he had a policy, probably wouldn't pay either because insurance often doesn't apply to criminal or intentional acts, Zimmermann says.

“You can sue the thief, but good luck,” Zimmermann says. “Even if you win, the chances of recovering any money damages are slim.”

In some states, the car owner might be found at least partially liable if he did something negligent that led to the theft, such as leaving the keys in the car with the car running, Reischer says.

Or your own uninsured motorist insurance, which covers your injuries if an uninsured motorist causes an accident, might kick in.

“Uninsured motorist coverage is something people don't have enough of,” Zimmermann says. “They'll buy $100,000 of liability coverage and only $25,000 of uninsured motorist insurance. When they do that, they're protecting other people more than themselves.”

5. A driver hits a deer, loses control of the car and crashes into you.

“Sometimes you can have an accident in the true sense of the word — where no one is at fault,” Zimmermann says.

This could be the case if a deer appeared out of nowhere and leapt in front a vehicle, causing it to crash into someone else.

But Simeone says the other driver could be at least partially liable if he did something careless, such as drove too fast.

Finally, keep in mind that liability isn't always an either-or proposition. In states with comparative negligence laws, liability is calculated on a percentage basis. One party might be 30 percent liable, and the other party 70 percent.

The insurance company's decision isn't final. Depending on the state and the claim, you can take the case to court.

“You can sue anyone,” Zimmermann says. “The question is can you win.”