Do you have to have full coverage auto insurance?

No, "full coverage" auto insurance is not required by law.

All states require some level of car insurance that covers costs if you are responsible for an accident. That would be called liability insurance and the state minimum coverages dictate how much of it you need to buy.

That said, "full coverage" does not actually exist and the phrase generally refers to buying a combination of several insurance types to ensure the most protection.