Self-employed persons can deduct health insurance premiums above-the-line. This deduction is available to independent contractors, and owners and partners running small businesses.
Auto insurance might also be deductible, if you drive your car or truck for business purposes. Generally, the deduction for car and truck expenses is available for self-employed people who drive for business, or employees who use their own vehicle as a part of their job. Your daily commute to work is not tax-deductible, but there is a notable exception for people who have to travel extraordinary distances to get to their job site.
Also remember that you cannot take a double tax benefit for an expense. So if you receive a reimbursement for property damage (which is a tax-free event), you'll be able to deduct casualty losses only for any damage that remained unpaid by your insurance.