I certainly recommend to check a used car history records before buying a car.
I tried CARFAX vehicle history report service many times and found it very useful. It doesn’t give you a 100% warranty that the car is perfect, but for sure, spending a few dollars for a history report can save you a lot more. You may find out the following:

• Totaled in an accident/Salvaged
• Flood damage
• Odometer rollbacks
• Lemon histories
• Junked Titles
• State emissions inspection results
• Lien activity, and/or
• Vehicle use (taxi, rental, lease, etc.)
• Service and repair history
• The good thing, CARFAX works in Canada as well.

Why do you think the body shop keeps that rear piece of the car? Because when they find the same vehicle with rear end damage, they will just weld one car from two pieces, paint it nicely and sell it through the auction somewhere in a different state or province. Soon it may appear in a used car dealer lot as “Immaculate condition with low mileage”. The car may look clean and shiny, but if you check the car history report, you may find that the vehicle was salvaged.
Another example: I received a message from the person who recently bought privately a “low mileage” car. He even had it inspected by a dealer and had been told that the car is OK. Few days later he found out that CARFAX report shows much higher previous mileage. Very unfortunate situation. By the way, when you bring the car to a dealer for inspection, have a look at items covered in the inspection checklist – usually it does not include things like previous accident check or odometer fraud check. Thus, even if you have a car inspected by a dealer, check history records BEFORE buying a car.