The amount of auto insurance coverage you need depends on a variety of different factors. When choosing your coverage limits and deductibles, consider the various risks that you, your passengers, and your auto are likely to face. You also need to consider the assets you own, which your automobile insurance coverage helps protect.
Any insurance agent worthy of their salt will tell you that you should buy as much as you can afford.
If the other driver involved in an accident is underinsured, this coverage typically pays any difference between what the other drivers insurance covers and what your bodily injury coverage will pay. The coverage limits refer to the maximum amount that will be paid per person, per incident, respectively. If the limits you purchase are lower than an accidents costs, you'll be responsible for paying the amounts over your limits, unless you're covered by health insurance.
Individuals without health insurance may benefit from Uninsured/Underinsured Motorist Bodily Injury, because if the limits chosen are inadequate, you'll be responsible for paying the additional amount.
In some states you can purchase Uninsured Motorist Property Damage. It is recommended that you purchase Collision coverage on your vehicle to cover physical damage. UMPD covers when property damage is sustained by an insured and the at fault driver has insufficient limits of liability to cover the damages to your property. If you don't have Collision coverage, Underinsured Motorist Property Damage coverage pays up to a certain amount for repairs to the insured car (some states have limits at $3500, some are lower and some are higher). If you have Collision coverage, Underinsured Motorist Property Damage coverage only pays your Collision deductible (in some states).
Underinsured Motorist Property Damage alone is not enough to cover all potential car repair/replacement costs, and only applies if you are involved in an accident caused by a driver without enough liability insurance coverage.
You can get a car insurance quote here to determine how much it would cost for different levels of coverage.