However, practically every state has enacted insurance laws that require drivers to carry at least some auto insurance. Many states even require that you present proof of insurance before you register a car. So the short answer to the question is that you will probably need to
insure your car, regardless of its value.
Every state requires that drivers carry liability insurance.
The liability coverage section of an auto insurance policy provides financial protection from liability claims against you when you (or certain other people) cause an accident that results in bodily injuries to other people and/or damage to their property. Every state has mandatory minimum levels of coverage in this area. The rationale behind such laws is that at-fault drivers should be able to compensate victims who suffer accident-related losses. But the required minimums in most states don't even come close to covering the costs of a serious accident. Consequently, if you wish to be adequately protected from liability claims, your liability coverage should probably exceed your state's requirements.
Other coverages are required in some states and optional in others.
Medical payments coverage and uninsured/underinsured motorist coverage are two such coverages. Medical payments coverage covers medical expenses incurred by you, your family members, and your non-family passengers. Uninsured/underinsured motorist coverage covers losses you and others suffer as a result of an accident caused by a driver who either has no insurance or insufficient insurance. If buying these coverages is optional in your state, base your decision on your needs, circumstances, and other factors. Consult your insurance agent for more information.
Collision and comprehensive insurance is optional in virtually every state.
The collision and comprehensive section of your policy covers physical damage to your own vehicle resulting from collisions and a variety of other causes (e.g., fire, falling objects). It may also cover losses associated with theft. However, your car's value plays a big part in assessing your need for this type of coverage. It may not be cost-effective if your vehicle is worth less than $1,000 because you'll have to satisfy a deductible, and the most you'll receive (even if your car is totaled) will be its actual value (i.e., after depreciation). That's not much, especially taking into account the premiums you would have been paying for coverage.