An article from Morrison Remodeling called "How to Select a Remodeling Contractor" says:
Workman’s Comp insurance compensates the contractor or one of his employees if they are injured on a job. It pays for their medical expenses and gives them a substitute weekly salary until they are better. It is required for all contractors if they have employees. If they are sole proprietors and work alone they are not required to have it by law, but they should have it anyhow, to protect you.
So, should you hire a contractor without workers' compensation insurance? Maybe. In some fields, like computer repair and handyman services, few providers will have workers' comp.
What's the risk? If you hire a contractor without workers' comp, and if he or she is injured on the job, and if the injury is serious (expensive), and if he or she decides to sue you, and if the court finds against you, then you may owe a lot of money.