The laws vary by state, but most require basic liability coverage. States want to be sure that motorists have some financial backing in the event of a collision or any insurance-related incident. Most states require insurance to operate a vehicle in any circumstance, but there are a few exceptions:
Tennessee and Wisconsin do not require liability but legally expect drivers to prove adequate "financial responsibility" in the event of a collision. (Source: TN, WI DMV websites)
New Hampshire initially requires no insurance but does temporarily after a collision. (Source: NH DMV website)
Virginia is a rare exception, allowing a driver to pay a $500 Uninsured Motor Vehicle fee to legally operate without insurance at his/her own risk. However, the fee expires with the registration and must be renewed. Drivers in Virginia opting for insurance must meet the state's minimum coverage. (Source: VA DMV website; http://www.dmv.virginia.gov/webdoc/citizen/vehicles/insurance.asp)
Drivers in these four states often still carry insurance as protection.