You need to distinguish between what the law says you must do, and what your risk-tolerance says that you can do.
If you have employees, you must pay worker's comp and taxes for them: you can get in a mess of financial and legal trouble if you don't. If you only occasionally hire a laborer, a worker's comp policy may be too expensive - some worker's comp policies have a minimum annual premium in the thousands of dollars, which would cover maybe $20K of labor cost. If your annual labor costs are lower, you can stay legal by hiring through a payroll service or temp agency that will pay taxes and workers comp for you.
You should also pay your own taxes, of course.
General liability insurance may be less about legal requirement than financial risk. Different states have different requirements. In California you don't have to carry it, but I believe that you need to inform residential customers whether or not you do.
G.L. can be expensive - you can get a nearly instant quote from an agent to find out how much - and most carpenters and contractors starting out, who don't have much on the way of assets, probably don't carry it at first. If something goes wrong, insurance companies or customers may not come after you if they see that you have no assets. To some extent you can manage the risk by taking appropriately small jobs. If you take on house framing jobs your liability exposure is significant, and G.L. really makes sense. Most guys doing the occasional door replacement as a side job, or starting off doing interior finish work, probably don't carry G.L. See what your state requirements are.