The range of credit score and other qualifying factors needed for a no-annual-fee credit card will vary by card issuer. If you have a credit score of about 700 or above, you will likely have little trouble getting your pick of fee-free credit cards. If you don’t have as good of a credit history, you may face challenges getting approved by some of the most selective card issuers. However, there are secured credit cards that don't charge an annual fee and that almost anyone can qualify for by placing a security deposit to act as collateral. These kinds of cards can be very helpful when it comes to building credit and potentially improving your credit score.