None of these tricks in this forum (or others) worked for me. The Apple Support Team told me my only option was to enter Credit Card information, then delete it later. However, after 15+ aborted attempts to "Review" my newly created Apple ID (on a mix of iTunes, iPhone Apple Store, and web browser based Apple login sites) and hitting the wall over and over, something happened and the "None" button showed up during the Review step when I got to the stage where it wanted my Credit Card information. I wish I could be more helpful, but after so many failed attempts, the best I can recall was that I went in for try #16 and did the following steps:
1) Using iTunes (on a Windows PC), I went to the Apple Store (top right button on my version of iTunes) and signed in using my Apple ID/pwd,
2) I think iTunes just forced me into the "Review" loop again immediately (but perhaps I tried to download a free app...regardless I got back into the Review loop),
3) I went through the first few Review screens (name, birthday, whatever),
4) When I got to the payment entry screen, I still did not see the mythical None button, but decided to click on PayPal for fun,
5) This seemed to launch a background browser tab for logging into PayPal, but I ignored that (I ended up just closing that tab some time later),
6) <FUZZY MEMORY> Back in iTunes, I believe I tried hitting Continue (Next?) button at the bottom without any Credit Card info,
7) <FUZZY MEMORY> I believe I had to exit/cancel this particular Review Loop...however, possibly it was this same loop session when the None button appeared at the top of this entry page next to the other payment options after hitting Continue (and failing)...I just had to add my Title and phone # (?) and then Continue/Next did work.
8) <FUZZY MEMORY> If what I recall in #7 above isn't exactly right, I most likely just cancelled that Review loop where I got stuck again but after hitting PayPal, and simply started a new 17th Login/Review loop: Again in iTunes, logging in to the same Apple ID account, going through the same first screens (#3 above), and then this time when I got to the Credit Card entry screen again the None button was actually available and working (after entering Title, etc.).
9) I recall that the iTunes Review process seemed to simply just end after this...I don't recall seeing a "Success" message, but I was done and my account is working fine, no Credit Card (or PayPal) information was entered!
Sorry I can't be more helpful, but I hoped that by posting this it might get someone started and they can fill in my blanks. Best of luck...it is possible!