Many successful indie authors do not use ISBNs (for their e-books), and they see no reason why they should. The number Amazon provides works just fine from a practical standpoint.
Having said that, an ISBN gives your book added credibility and has more universal recognition than an ASIN (Amazon Standard Identification Number) when searching for a book by number. So I opt for an ISBN.
However, buying an ISBN costs money. In the United States, buy ISBNs from Bowker. Currently, the standard price for one ISBN is $125, ten costs $295, and one hundred costs $575.
Note that you will need one ISBN for each format your book is in: Hardcover, paperback, e-book, and audio, so that’s four ISBNs. Given the costs, I see why many indie-published authors skip them.