There are two types of inquiries that can be made to an individual's credit report - “hard” and “soft”. An inquiry is when a company requests access to your credit history. If you are applying for credit, the company will perform a “hard inquiry”, which typically results in recalculation of your credit score. The more hard inquiries you have the lower your score will be – and if you are already starting out with less than perfect credit, a hard inquiry will ding your score more than someone with great credit before the hard inquiry occurs. Other inquiries to your credit report that are not used for lending decisions are considered “soft inquiries” and are generally used to gather information like confirmation of your identity.
That being said, opening a new deposit account used to only be a “soft” pull of your credit, but increasingly is becoming a common reason for a “hard” inquiry. It depends on the bank you are opening an account with, and is often difficult to know in advance whether the inquiry will be a 'soft' or 'hard' inquiry of your credit history. You might try asking before applying, but in some cases the person helping you open your deposit account will not even know for sure!
A forum on FatWallet.com has started a list of banks and users have been submitting details as to whether each bank does a hard or soft pull of your credit for various bank accounts opened. You might want to check the list if you are concerned with the number of hard inquiries your credit history has been getting prior to opening a new bank account.
According to the consumer-created list on FatWallet, it seems none of the most popular online banks are using hard inquiries for opening savings accounts, but banks offering money market and checking accounts are regularly doing hard pulls in an effort to figure out how much overdraft protection you should be allowed as this amount is directly tied to your credit score.