Does every company have to have workman's comp coverage for its employees?

If state law requires it. Some states do not have laws requiring businesses to have such coverage. Other states have limitations such as the number of employees, type of work, etc.

Another issue is the type of occupation. For instance, Firefighters and Policemen have their own 'plans of coverage' for on-the-job injuries.

Some other occupations may also fall into this "TYPE" of situation. Off the top of my head, however, these are the only two coming to mind.

Even if the state has an exemption AVAILABLE (number or type of employee) the employer remains liable, so exercising the exemption is not wise unless you have funding available to pay a claim. An option in most states for *some* workers is Occupational Accident coverage, which can provide many benefits similar but not equal to Workers Compensation coverage.