All states except New Hampshire require you to carry a minimum amount auto insurance on registered vehicles. So, if you plan to keep driving, you'll need to maintain your coverage.
But what if you plan to stop driving your car just for a period of time? Then, you have two things to consider:
Whether you can suspend it depends on state regulations, the insurance company's stance and the lender's requirements if you have a loan on the car.
Because all states (except New Hampshire) require you to carry insurance on registered vehicles, suspending coverage means you might also have to suspend or cancel the registration, then reinstate it later. Some states have a procedure for doing this, but it might be more hassle than it's worth.
Meanwhile, your insurance company may or may not allow you to suspend your car insurance coverage. Finally, check the loan documents if you took out a loan to buy the car. Sometimes lenders require you to carry insurance on the vehicle and don't allow coverage suspensions.
Also, consider the consequences of suspending your coverage. Although the car will be safe from traffic accidents because you won't be driving it, it could still be at risk for damage from other causes, such as a hailstorm, flood or vandalism. Or, it could get stolen, especially if it's parked outside an unoccupied house for months. Comprehensive and collision insurance protects you in case of theft or damage from events others than traffic wrecks.
Because of these risks, it's probably a bad idea to suspend the entire policy. If you're keen on suspending it, see if you can suspend portions of the policy and maintain comprehensive insurance.
What if your insurance company doesn't let you suspend coverage? Don't even think about not paying the premium and letting the insurer cancel it. With a cancelled insurance policy due to nonpayment on your record, insurers will consider you a big risk. You'll pay higher premiums as a result once you're ready to purchase another car insurance policy – even if you go through a different company.