Can I suspend car insurance for several months?

Do not suspend your insurance. First, in many states, it's illegal to own a car without insurance. Second, if you suspend your insurance and then need to have insurance again, it could cost a lot more, because insurance is much more expensive, sometimes thousands of extra dollars, so someone who has not had insurance at any time during the previous few years.

Do ask your insurance company if they can give you a break in the price of the insurance, since you won't be driving the car.

If the car is financed then no you cannot do this, if you own the car completely then yes you can do this if car is on private property. But do be aware if anything happens due to storm, fire, theft, etc. the car will not be insured unless you keep comprehensive insurance. At that point you will save very little money. I will not be able to drive my car for at least 2 months or more (and I own the car, its not financed) but be assured it is fully insured even if not driving it. All your choice.

In most states if you car is currently registered it need to be insured - if you want to turn in your plates and registration you could then cancel your insurance (given you don't have a lien).