Just because a car has a clean carfax, doesn't mean it's a good car. While it weeds out about 95% of the bad ones, there are ways around. Google the VIN first, see what's out there. Look for any websites that could be auctions, junkyards, reconditioners, etc.... I was looking for a Camaro 2 years ago and the car had a clean carfax...that's all because the first picture was Monday, the second was taken on that Friday at the dealer before carfax caught up! I found it by just doing a VIN search on Google!
Also, it's been reported that competing vehicle history companies can produce different results, so it is recommended that used car buyers purchase vehicle history reports from more than one vehicle history reporting company.