Actually, it's very unlikely that any type of car insurance would be canceled after you file a single claim. However, filing a claim could increase your premium on certain types of car insurance.
In most states in the United States, and in many countries around the world, the motor vehicles department has a "point" system, which is used to track accidents and violations that affect your driving record. Car insurance companies will order a copy of your driving history once you have purchased a car insurance policy, in order to confirm the information that you provided on the application. Your company may also check your driving record when your car insurance policy is scheduled for renewal.
Like many dual-income couples, you and your spouse may have both included your kids on each of your group health insurance plans. However, without some sort of system in place to help the insurance companies coordinate benefits, it's possible that either you or your doctor would be reimbursed for more than 100 percent of the actual cost of your claim.