I have read The Godfather, The Last Don, Fools Die, Omerta, and started to read The Family.
Absolutely loved The Godfather, so much detail, such a rich story and rarely does a page go by that isnt captivating. A few drawn out parts, but remember, this was a book before it was a movie.
Second favorite read has to be Fools Die. Every character is interesting, every story has a point and is fascinating.
Last Don and Omerta are very good reads and are more of a current state of the mob stories.
Couldn't quite get into The Family. I'm sure I will re-visit it sometime soon, but it was a struggle to read the limited amount that I did read.
Some other non-Puzo great reads are:
Gangster, Lorenzo Carcaterra
King Con, Stephen Cannell
The Plan, Stephen Cannell
Motherless Brooklyn, Jonathan Letham
Donnie Brasco, Joseph Pistone
Underboss, Peter Maas
and a few other non-fiction/true crime books about the mafia. have a library of over 40 mafia related books, so if you have any questions about a particular book, just ask, chances are I've read it.