There are tons of posts talking about how to create an Apple ID without a credit card but none of suggestions that I tried work. Finally I gave up trial and error using my iPhone. I went back to my PC using iTune 10.x instead. Here are my findings.
My iTunes Version: iTunes 10.x
Regardless of how you register your account with apple for appleid, "NONE" payment option most likely won't be available if you don't sign up one with a Free App. I don't know why. It took me a few trials so as to figure out, which consumed me a few email addresses to confirm this.
Second, if you initially sign up one Apple ID without "NONE" payment option to begin with, there is no way for you to make "NONE" appear after your Apple ID has been created. Therefore, be sure, you sign up for a new Apple ID with a free app, such as Chrome or go to iTunes Store, click on Free on iTunes and then select one free app to continue. It is how I got my few Apple IDs with NONE payment option.
Is this NONE option related to certain countries? I have no idea. I don't bother to find out either. If you don't see the NONE option, "cancel" it and then start over: scroll down your iTunes Store window all the way to the bottom and then click "Change Country" to proceed. For sure, the United States works! From the Google search, besides the US, United Kindom, Hong Kong, Japan, and India also are claimed to have "NONE" option available.
I don't understand why Apple doesn't fix it or it may intent to make it difficult.