ISBNs were a mystery to me until recently, so I thought I'd take a few moments to share what I've learned and see if anybody had any advice or tips to share. A lot of the information I could find was somewhat out of date, and I think that's because things have changed so much in recent times.
So, the basics. ISBN stands for International Standard Book Number. An ISBN is a unique number assigned to a book in order to help people find it. It contains the publisher's code, and the code of the country in which the book was published, and then some unique numbers to indicate the book itself. This makes it easier for computer databases to retrieve information about your book.
However, places like Amazon and B&N don't require an ISBN; they use their own identification code to track the books through and in their systems. You can also use their numbers to find your book on sites like Goodreads.
Smashwords gives a free ISBN to any book which qualifies for its premium catalog, but this lists them as your publisher. However, they don't claim any rights to your book because of it. Also, the ISBN given by Smashwords isn't to be used at Amazon or B&N, if you publish there yourself (which is quicker and quite easy, for the most part) rather than letting Smashwords distribute to them.
You also have the option of buying an ISBN from Bowker directly, and this ISBN would list you as the publisher. However, a single ISBN runs about $125. You can buy a batch of 10 for $250, which is suspiciously deep discount, if you ask me.
It's possible to never have an ISBN attached to an ebook and still sell it through Amazon, B&N, and Smashwords, but it won't go out through Smashwords to the Apple Store or Kobo. However, each format requires a different ISBN, so if you put your book out in print later, you'll need to get an ISBN when you put the print edition out. If you want your book to be in bookstores or libraries, you must have an ISBN.
So, there's a lot to consider. Buying an ISBN directly from Bowker means that you are listed as the publisher. There's debate about how important that is, though. Some claim that books listed as published by Smashwords may be a turn off to readers, while others say that this is offset by having your title distributed in as many places as possible (such as the places Smashwords will only send it if there's an ISBN attached).
Regardless, you will need to purchase a separate ISBN if you do a print run of your book, and places like Createspace offer a similar (if I'm not mistaken?) service, allowing you to purchase an ISBN from them at a fraction of what you would pay at Bowker. The question of whether it's better to purchase from them or directly from Bowker may come down to the particular perspective of the author.