Yes, a 17-year-old normally can get car insurance, but since they are minors, a parent or guardian typically will be required to sign on the policy with the teen.
For a complete guide to insurance specifically for 17-year-olds, including average rates by state, read Car Insurance for a 17-year-old.
In general one must be an adult to obtain an insurance policy on their own, so 18 years of age or older. If you are under 18, and thus still considered a minor, then normally state laws and insurance companies' guidelines will require you to have a parent or guardian sign on legal documents, such as an insurance policy, with you.
Typically if you are old enough to have a driver's license or own a car you can buy an auto insurance policy. If you are a minor, your parent or guardian will usually have to sign on the insurance contract with you though.
If you are a minor and what to own and insure a vehicle you should check with your state's Department of Motor Vehicles and insurance regulator to see if there is a minimum age set and what extra measures you may need to take until you become 18 and considered an adult.