Almost without exception, you do need car insurance. This is not a federal law, but state laws. The minimums vary for each state, but every state requires some type of car insurance.
The minimum laws in each state lay out how much insurance one must carry per passenger, per accident and property damage liability. For example, California car insurance $15,000/$30,000/$5000. Meaning, at the minimum, one must carry $15,000 per passenger, the maximum insurance claim on an accident is $30,000 in medical claims, and $5000 in property damage. The minimum insurance is often called PLPD insurance.
It is important to remember that these are the minimums. For most this amount will not be sufficient. Just because the minimum insurance is defined, your liability is unlimited. You will be personally responsible for all damage, whether covered by insurance or not.