The National Insurance Crime Bureau, an anti-fraud group made up of hundreds of insurance companies, car rental companies, auto auctions, etc., runs a free online site where you can check to see if the car you're about to buy has been reported as stolen or salvaged.
It's called "VINCheck." You type in the vehicle identification number. On most modern cars, the VIN is usually a long combination of numbers and letters on a plate or tag at the front of the dashboard. It's easily read from outside, through the windshield.
VINCheck will tell you if the vehicle has been reported as stolen and unrecovered, or if it has been reported as a salvage vehicle, by participating NICB members.
A maximum of five searches are allowed from each IP address per 24-hour period.