If you are an independently published author who wants to self-publish professionally, you absolutely must buy your own ISBNs.
DON'T BE TRAPPED
When you buy your own ISBNs you'll never be trapped with an unscrupulous author services company (like those offered by Author Solutions companies), who charge much too much for services and mark up the print copies of your books.
Which book formats need their own ISBN?
You'll need one ISBN for your hardback, another for your paperback, and stilla another for your ebook. If you create an audiobook, that's a fourth ISBN. It doesn't matter where you distribute - it's the format that counts.
Paperback: Your paperback printed and distributed by Amazon CreateSpace to the Amazon store should have the same ISBN as the one you upload to B&N or IngramSpark. If you got a free ISBN from CreateSpace... well, that was a mistake, so just keep it and apply your own ISBN to the book you upload to IngramSpark or elsewhere.
Hardback: No matter where you print and distribute your hardback book - if you create one - you'll use the same ISBN for that, too. (I recommend IngramSpark for hardback book creation and distribution.)
EPUB: When you distribute your ebook (choices include BookBaby, Gatekeeper Press, IngramSpark, Smashwords, StreetLib, Draft2Digital) you'll need one ISBN for the EPUB version. That EPUB will be sent to Amazon, who will create a Kindle file from it, so you do not need a separate Kindle ISBN.
Kindle: If you upload your ebook to Amazon KDP directly, you'll need a separate ISBN for the Kindle (MOBI) edition.
Audiobook: Another ISBN gets assigned to the audio edition of your book, too.
Special editions: If you create a special, custom edition of your book with images, links, multimedia, etc., that's one more!
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Purchasing Your ISBNs
In the US, authors should go to the Bowker My Identifiers site and sign up for an account. Buy 10 ISBNs for $295 or 100 for $575. It costs $125 for one, and you'll need two or three for the various formats. (More on that down the page.)
In the United States, ISBNs are expensive. In Canada, they're free. Use your search engine to find your country's ISBN registrar.
Look professional to bookstores
You also need your own ISBNs to obtain an LCCN and PCIP block for libraries. You may not aim to distribute to libraries but if you want your book to look exactly like those published by the Big 5 publishing houses, you'll want a CIP block on your copyright page.
Find out how to make your book look just like those from the traditional publishing houses in my post 20 Rookie Interior Book Design Mistakes to Avoid.
The freedom to change
A "free" ISBN is never free. It comes with a price. I've helped many authors extricate themselves from Author Solutions and other predatory self-publishing services who own their book data, to take back their freedom to choose where they will publish their book. Purchase your own ISBNs and you'll never be trapped.