Lightning Source (LS) is the dominant on-demand book printer. I've used the company for many of my books. LS does good work at a reasonable price, and will make books quickly available at Amazon.com and many other booksellers around the world.
I recently discovered that LS may treat the publishers who use it as second-class citizens, compared to booksellers.
On December 8 I ordered eight copies of the hardcover edition of my Stories I'd Tell My Children (but maybe not until they're adults). I need them for gifts and to send out to be reviewed. As of this mornng, LS shows the order status as "printing" -- six days after I placed my order.