I came across information about ChexSystem via The Dough Roller.
From DR:
Have you ever been turned down for a checking account? While denials are more common when applying for credit, you can also be declined when applying for a bank account. If you have been declined, it’s likely due to a reporting agency that many have never heard of, but who has a lot of information about and influence over banking customers. It’s called ChexSystems.
Most have heard of the three major credit reporting agencies–Experian, Trans Union, and Equifax. But there is a lessor known but equally important reporting agency for checking accounts called ChexSystems. Run by Chex Systems, Inc., ChexSystems provides account verification services to its financial institution members to aid them in identifying account applicants who may have a history of account mishandling (for example, people whose accounts were overdrawn and then closed by them or their bank).
Check out the link for more info about ChexSystem.
Here is something useful from their FAQ:
How can I opt-out of pre-screened offers of credit?
Under the federal Fair Credit Reporting Act (FCRA), consumer credit reporting agencies are permitted to include your name on lists used by creditors or insurers to make “pre-screened” offers of credit or insurance that are not initiated by you. The FCRA also provides you the right to “Opt-Out”, which prevents consumer credit reporting agencies from providing your credit file information for “pre-screened” offers. If you choose to opt-out, your name and address will be removed from the lists these offers are based on. You may opt-out with the nationwide credit bureaus at 1-888-5 OPTOUT (1-888-567-8688). You may opt-out with ChexSystems at 1-877-OPTOUT 5 (1-877-678-6885).