No, but is a rare situation that would not require some insurance.
If you are working as a subcontractor and the contractor above you advises it is not required and then lists you as an "Additional Insured" on their liability policy then purchasing further insurance is your choice. You can buy insurance for your tools, equipment, business interruption and the like. You can also buy liability insurance to increase the total amount of a claim payout if needed.
If you deem your possibility of loss to be so low then you might choose to self-insure. If your customers do not request proof of insurance then you might think that insurance is not necessary. Think about what could happen. How likely is it that this will occur? If it does go wrong, how severe will be the effect?
Do you sit on a volunteer board? If so, does the board have director's and officer's insurance for the members? Do you control volunteers? You could face a court case regarding human rights and would bear legal costs yourself if you do not have insurance.
Business insurance transfers the consequence of financial loss. If things do go wrong then the insurance company will pay. Even this transfer will have limitations and conditions.
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