Always, always, always test drive the car. Be sure to keep the radio off while you are driving the vehicle so you can hear any odd sounds. Test brakes, acceleration, anything "power" such as windows, locks, moonroof, etc. Look under the hood for any visible signs of oil leaks, worn belts, corrosion, etc. Inspect the outside of the car looking for things such as uneven wear on the tires (alignment problems), check all of the side panels and doors to make sure that each piece bears the stamp with the vin number that matches. If the car has been in a serious accident, usually replacement parts have been used from salvage vehicles and you can usually spot this. Many manufacturers also use a stamp on their glass so you can check to see if the car has all of the original glass. You can also check the Carfax report although this will only show you certain information. Always try to buy a car with at least a portion of the original factory warranty remaining so you can have any repair work done by the dealership without investing additional money.