It varies by state, but most carriers will require it. Most states require people to be covered under Worker's Compensation, although business owners (like independent contractors) aren't employees, so the alternative is Occupational Accident Insurance.
Ballpark is about $30 a week. It covers you for any accidents you may have while under dispatch. When you're not under dispatch you are not covered, in the same way that at a regular job you are covered by Worker's Compensation when you have an accident at work, but not when you have an accident after work while at home.
OOIDA has OAI plans. I get mine through my carrier.