Yes, an insurance claims database does exist and it contains data on all your claims besides other personal information. The database is called CLUE. This database is used by any of the insurance companies to decide if you are a viable risk or not. Not only does it cover any claims you might have made, or merely inquired about, but it includes personal data. For instance, did you lose your job or were you unemployed for a while? CLUE is a national database which can be tapped into by any insurance company, except in certain states which now are now looking very closely at this use of personal data. One has to wonder where the privacy laws are being overstepped.
For more info, see How Claims Affect Your Auto Insurance Rates