Q: My iPhone will not download free apps without a credit card. Why is this?

Hello Kelly,

You may need to change your payment information to "None" in account settings on your iPhone.  I found an article with these steps:

Changing your account information using an iOS device:

1. Tap Settings on the Home screen.
2. Tap iTunes & App Stores.
3. Tap on your Apple ID. (If you are not signed in, enter your Apple ID and password, and tap Sign In.)
4. Tap View Apple ID.
5. Enter your Apple ID password.

To update your name, billing address, or payment information, follow these instructions:

1. In the Edit section, tap Payment Information.
2. Update the information that you want to change.
3. Tap the Done button when finished.

Note: The payment methods that the iTunes Store accepts can be found in the payment type section. If you do not want a payment method on your account, select None in the payment type section.

You can find the full article here:

iTunes Store: Changing account information

http://support.apple.com/kb/ht1918

Thank you for posting in the Apple Support Communities.  

Best,

Sheila M.