I have been having the same issues. First it told me that my security code was invalid/incorrect, however, it was perfectly fine. My card is working fine. There is plenty of funds/availability on my card and there is no issue with my card/bank.
Where I am having a problem in that Apple automatically adds 4 digits to my zip code which my bank does not use. So Apple thinks it is the wrong address, however, it is Apple that has it wrong and they refuse to override this and correct it so that it matches the information that my financial instiitution has on file.
These four digits are automatically added to your zip code even if YOU DON'T TYPE THEM IN yourself. When you hit "done" they will be added, and if your financial institution does not use the full nine-digit format for your zip code, you will not be able to use that card. I have contacted Apple about this multiple times over the past two days via online chat and phone, and they refuse to do anything else to help me, other than suggest I make all of my information with my financial institutions conform to the *Apple Way*.
As recommended by other posters, I have also attempted to use the PayPal option as a work-around. This works fine on PayPal's end, as I receive the confirmation from PayPal confirming that I've created a payment agreement with Apple, however, when I click "done" on the Apple page, I get an error message.
If you go to the iTunes Store discussion forum, there are many, MANY people who are having the same issue and the only response is some "cut-and-paste" response about making sure your information in Apple matches the information at your bank. No other solutions are offered, because, well, there aren't any (although the cut and paste fails to point out this "extra 4 digits to your zip code" issue that many people are simple not even noticing because it happens AFTER you hit "done")...
If you find any other information, or if anyone else has anything to add, please do so. I would like to be able to download the $19.99 app that I'VE ALREADY PAID FOR OVER THE PHONE but can not download because Apple won't accept either of the two perfectly good methods of payment I've offered, that aren't even necessary for this activity because I've already paid for the download in FULL (and, yes, I have my bank statement to prove it).
https://discussions.apple.com/thread/4228263?tstart=0