Perhaps the most important insurance coverage to make sure that your contractor has is workers' compensation. Rules vary by state, but in South Carolina, anyone employing 4 or more people is required by law to carry workers comp insurance. If they have fewer than 4 employees, even down to a sole worker working alone, they can (and should, from the homeowner’s perspective) carry worker’s compensation insurance.
In a nutshell, workers comp insurance is your prevention from the risk of being sued if any worker doing work on your property is injured on the job (or claims to be injured). If your contractor has this insurance, then the coverage amounts allowed under state law apply. The employee cannot sue their employer, or you, for more than is paid under the worker's comp rules. However, if there is no coverage, then all bets are off, and the employee can sue their employer (quite likely putting them out of business), as well as the owner of the site (you), and anybody else with deep pockets to pay their costs.
Sole workers like carpenters whom you hire, and who work alone, can be tricky since they are not required to be covered and rarely want to spend the money for the insurance. But be aware that if there is a serious on-the-job injury, their livelihood may be gone, and suddenly their lawyers will argue that you are actually their employer and are liable! Also bear in mind that workplace injuries can be extensive and even permanent – and often very hard to prove, like back & neck injuries – and can result in huge long-term liabilities.
I run the risk of being alarmist on this subject, but insurance isn’t there for when things go right, it’s there for when things go wrong. While the odds are that nothing like this will happen on your next home improvement project, is it worth the risk to cut corners? The costs to provide proper insurance are significant to the contractor – they could increase the cost of your project by up to 5% to 10%. But the risks on larger projects, especially those done outdoors and projects involving multiple workers and helpers, are very real.
One final comment – how do you know that your contractor is insured? When selecting a contractor you should ask to see his Certificate of Insurance. This is a standard form document provided by his insurance company or insurance agency and specifies the amounts, as well as the date of coverage. Normally a reputable contractor will be eager to provide this document – he wants you to know that he is conscientious about protecting both himself and you. So don’t feel uncomfortable to ask. And don’t accept any excuses – the most important thing is to make sure that you and your family are protected.