Can I "purchase" a free book from the Store without providing a credit card number? There are a few books on Google Play that are free. Can I obtain said books without providing a credit card number?
Looks like it depends on the book. From Google Play support:


  Downloading free music, TV shows, and certain free books and magazines is still considered a transaction, even when the price of the item is $0.00. If you don't have a credit card associated to your Google Wallet account or if you don't haven't set up a Google Wallet account, you'll be prompted to add a new payment method upon when downloading certain content from Google Play.