What constitutes a "good case?"
For many reasons it is impossible to answer this question for all the many ways a person could become injured. The most common cause of injury, and therefore the focus of this guide, is negligence. In Washington, negligence occurs when a person (or other entity) (1) owes a duty to use reasonable care to prevent injury to others, (2) fails to meet that duty, (3) and causes (4) harm. Thus a "good case" must meet each of the four requirements. For example, a person who sustains neck/back injury when their car is struck from behind by another driver probably has a "good case." Each of the four negligence requirements are met. (1) All drivers owe a duty to other drivers to use reasonable care to prevent injury to others, (2) striking the back of another's car is a failure to meet that duty, (3,4) so long as the neck injury was caused by the crash, the last two prongs have been met.
What should you do if you have a "good case?"
Contact an attorney! Insurance companies are driven by profits and in most cases have to answer to their shareholders. They are, under almost all circumstances looking out for their best interests--not yours. They will try to settle your case for as little as possible in exchange for your signature on a paper releasing your right to bring a claim. Attorneys who focus their practice on personal injury make their living by representing injured persons in their claims against the insurance company. Most all of them offer free initial consultations and only charge a fee if/when they resolve the case on your behalf. This arrangement is called a "contingency fee" agreement.