Just bear in mind, only about 15% of insurance companies report to car fax. And, if a repair was paid for by a customer out of pocket, there won't be a car fax record of that repair.
I know how weak it is. But it's a start. The one car I'm looking is such a good price i'm concerned about lemon or salvage title. Car fax will show that
Another source of info is the dealer. Most will look up the service history if you give them a call with the VIN.
Mine did a Car Fax for me when I traded for it, but as stated above it won't show any out of pocket repairs as my Bonnet looked faded some and I took it to have a paint and body guy that was referred to me by one of the tire techs who did the 4 wheel alignment check I had when I had the new Run Flats installed. It was his brother and he told me it was repainted with a cheaper type of paint and clear and showed me a tape line on the Bonnet next to the fire wall. So he is going to fix a small dent fixed that is just above the lifting handel on the boot and when he does that he will also do the Bonnet and front fascia along with de-crasing the headlights and will clear all including the headlights as he said it would last years as apposed to doing the headlight cleaner kits do as he said that only last a couple of months. He said it was probably done because of tree sap got on the Bonnet. And is charging $800.00 apposed to the first quote I got that was $1400.00!