The only coverage you must purchase is liability. However, if you are financing your vehicle (either through a loan or lease agreement), your lender will require you to have collision and comprehensive coverage as well so that it doesn’t lose its collateral for the debt if the car is damaged or stolen.
If you own your car outright (are not making payments), you do not have to buy collision or comprehensive, though you probably should to protect your investment if you have a late-model car in good condition. Many owners of older cars drop one or both of these coverages to save money if they don’t feel their cars are worth repairing or replacing.
Your state may have requirements related to other types of coverage, such as personal injury protection, medical payments or uninsured motorist.