Switching to mass transit or a van pool is a plus for your community and the environment. It can be good news for your family's budget, too. You may be paying more in premiums than you would receive if your car got damaged or stolen. If you're a young driver, see if your parents will add you to their policy. While the overall premiums will balloon, you'll probably be paying less than you would if you tried to get a policy on your own.
Young drivers can also get good-student discounts with some companies.
Make sure you pay your insurance on time. If you're canceled for non-payment of premium, it's going to be harder to find a company willing to cover you. Review your policy periodically and update coverage accordingly.