Quick correction on some answers.. (Which I thought banks didn't check credit either.)
I'm a personal banker, and at my bank (one of the largest banks in the US, just don't know if I can say the company name), when we go to open someone an account, it checks the 3 major credit reporting agencies, and chexsystems. If they have horrible credit, below 500, they are not elegible for a regular checking account, but a different account type that has many restrictions on it. However, if there is a joint applicant and they are approved, we can chose to put the approved person as the primary owner (which only means your responsible for tax if any interest is gained). But as you were warned.. Be careful when adding someone to your account, it legally makes it their money as well and can do as they wish with it, or can have levys placed on the account.