Take a look at the Declarations Page of your automobile insurance policy. It may say "$50,000.00 per person/$100,000.00 per incident. This amount could be higher or lower (many states have statutory limits).
In any event, review this information and discuss it with your insurance agent or with a personal injury lawyer to make certain you are covered completely in the event of an accident. Get the highest limits you can afford!
Research Your Automobile Insurance Company
Nowadays, this information is readily available on the Internet so compare your company and its reputation for paying claims, disputing claims, and such.
In short, buy insurance from the company with the best reputation possible.
Make Sure you have adequate Uninsured Motorist/Underinsured Motorist Coverage
This is something that kicks in if you are involved in an accident with a driver who has no coverage or inadequate coverage.
Don't take chances. Much like your liability limits, make sure the UM/UIM limits are as high as possible.
Consider Other Coverage Options
Discuss with your insurance agent the possibility of a Personal Umbrella Policy, which would engage when all other coverage limits are exhausted.
Also, make sure you have enough coverage under the Medical Payments provision of your policy.