Always try to find a one owner vehicle. They are usually well maintained and the previous owner will have knowledge of all the vehicles' history.
Look for aftermarket parts that have been installed to increase horsepower. Many times this is an indication that the used car has been whipped. If you are looking for a fast car, try finding a bone stock one and upgrading it yourself.
Run a Carfax Report
. This will tell you the vehicles history.
Get the vehicle inspected by a professional mechanic. There are many potential problems with a car that cannot be seen just by looking it over. Have the transmission fluid checked to insure the tranny is not about to go. Have it checked over for indications of previous damage (including flood damage - Katrina damaged cars are showing up everywhere).
Be cautious when filling out the paperwork. Make sure the person selling the car is in fact the owner and has the title. Also be sure there are no registered liens against the used car.