Though states vary regarding insurance requirements (aside from the requirement that all vehicles must be insured), a general rule of thumb is to insure or list every licensed driver that has access to your vehicles. While the insurance carried will follow the car, the insurance company can revoke your insurance in some cases, or perhaps require you to exclude a particular driver from your policy. Insurance companies also have their own policies, and reading your insurance documents or asking questions will determine your coverages.
Most insurance companies will require you to either insure or exclude additional family members, especially teenage children. If your son or daughter does not have a license or permit, the requirement would be to sign an exclusion affidavit (A spouse is another example of required or excluded driver). Basically this gives the insurance company an exit should the teen be involved in an accident. Additionally, if your child is involved in an accident and are listed as an exclusion, you could be on the hook for thousands of dollars in damages, injury, and medical payments.
Insurance companies usually do not require that every person that ever borrows your car be listed as a driver. Your insurance will be loaned out with your vehicle, even if the person borrowing has their own insurance. The Borrower's policy will be considered secondary, meaning they will only cover costs that are above and beyond your policy limits.
When adding household members to your policy, considerations should be made. Adding others to auto insurance can be risky. If you decide to add someone to your policy, a good practice is to find out about their personal driving record, accident history, and of course license status. If you want to be certain, obtaining a copy of their driving record can be useful, although some may be reluctant or offended. Previous tickets, accidents, and claims can impact your premiums greatly. The best scenario for non-immediate family members or roommates is to require them to obtain their own insurance coverages prior to loaning out your vehicle.