Who asks for credit card?
An app that wants a credit card number is not a free app. Or the app uses in app purchases, which are linked to payment method.
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You have to add your credit card to open iTune or Google account. However, if you do not make any purchases of paying apps, there will then be no charges.
Unless you actually purchase "paid app's" in the Google app store(google account), there is zero need to enter a credit card number.
I get certain free app's and no credit card needed.
Nudges to sign up for "Google wallet" should be optional, when signing up for a Google account. There is usually a "not now button", or a remind me later button, next to the 'enter credit card' information section.
Google Plus is also optional, or can be deleted upon completion of email/youtube/smartphone account signup.
Google play no need for credit card at all for free apps. I will say however that the movie Big was recently offered for free for a limited time. When I "purchased" this movie for $0.00 it acted as if it charged my credit card.