This is a huge annoyance if you have more than 1 Apple device. Between an iPad, iPhone, Apple TV, Mac Mini, and new RMBP, having this prompt come up repeatedly is pretty crippling to an otherwise smooth iCloud experience.
The solution for me was pretty odd.
I use my middle name almost everywhere on the Internet, including my own contact list entry in Contacts. Since connecting everything together with iCloud (including my login accounts) Apple was seeing my account name as John James Jacoby, though your account can only have a First and Last name listed. Once I removed my middle name from my Contacts entry, the prompts stopped.
This leads me to believe that if something (I.E. anything) is out of sync, the default verification is the CVV2 code on the back of your Credit Card. You verify the card, it knows it's you, and the purchase goes through. The problem comes from us thinking it's the Credit Card that's incorrect, when it could actually be anything at all, and even something that the current applications UI doesn't allow you to change.
It seems like a bug, but an understandable one considering the complexity of Apple connecting everything together over the past few years. If you're still experiencing this issue, try making sure that all of your connected Apple account information matches between your iTunes account and your Contacts entry. Name, address, email address, everything.
For those of you that use multiple Apple ID's between devices, this gets exponentially complicated, and more likely to be part of the issue.