The Producers show bible/coffee table book is wonderful- the complete Broadway script, with lots of photos, pre and post production information and a ton of footnotes of alternate jokes and punchlines Brooks and company tried out. It's a must for anyone with a love of comedy, since it shows the way they fine-tuned the show's humor as much as the plot and score.
Paul W. Thompson, I don't know if this counts, but I have a trade paperback on Evita that came out during the show's first run (with Elaine Paige) in London. I haven't looked at it in years, but I seem to remember that it was written by Tim Rice and Andrew Lloyd Webber. It's about the real-life Evita and how they came to write a show about her.
About earliest single show books, while it's a "retro" book, and not for a then current production, I believe Show Boat: the story of a Classic American Musical came out in 1977.
I don't know the name and I can't find it via Google, but there is a wonderful book of black and white photographs, mostly from the seventies, eighties, and nineties that shows all these wonderful performers backstage in their makeup and costumes. It's both beautiful and eerie. I wish I could remember the title. There was a great one with Angela as Mrs. Lovett, Alan Cumming proudly showing an alcove he created off of his dressing room with lights and plants...
"Impossible is just a big word thrown around by small men who find it easier to live in the world they've been given than to explore the power they have to change it. Impossible is not a fact. It's an opinion. Impossible is not a declaration. It's a dare. Impossible is potential. Impossible is temporary. Impossible is nothing.”
~ Muhammad Ali
My favorite hardcovers are: At This Theatre, all of the Playbill yearbooks, the collection of NYT reviews (cannot remember the name right now!), and the Les Mis Stage to Screen.
My favorite paperbacks are: Seth's Broadway Diary, A Theatre Memoir by Martin Charmin, The Untold Stories of Broadway, and It's a Hit!
This may not be strictly Broadway but theres a hardcover book called "Streisand: In the Camera Eye" by James Spada and it has the most gorgeous photos of Barbra that I have ever seen. It includes some photos of her Funny Girl days. When I move out on my own the first book that will be set down on my coffee table with be that one along with The Untold Stories of Broadway.
Paul W. Thompson, I have the Beauty and the Beast coffee table book. It's hardback and features some nice photos from the production, though the writing doesn't really describe the creation of the musical so much as the finished product. I have books for all of the Disney musicals, and my favorite is the Aida one. Newsies is the only paperback one I have.
My favorite coffee table book is The Ziegfeld Touch. I got it rather recently, but the information and gorgeous photos more than make up for the lack of interesting writing. A must.