Carfax is not a substitute for having a prospective purchase checked out by a trusted mechanic. This usually costs less than $100 and will quickly uncover major issues like past accidents. I use Carfax as an added source of info when I'm buying, but understand the limitations of the data sources they use.
On their own website they state :
"Before you buy a used car, we recommend that you get a CARFAX Report, take a test drive, and have the vehicle inspected by a qualified mechanic. "