I own a hotel and had a look on booking.com for an API as I want to create my own front end interface to update my hotel room rates / numbers for some days. As well as upload pi
UPDATE 3 - 9th Dec 2017
It would appear that Booking.com now have documentation available for their API, but you need to be signed up to them as a business in order to get access.
UPDATE 2 - 8th May 2017
It seems Booking.com have recently completed some Beta testing for their API, it may looks like they are making it even easier for people to connect. For more information regarding Booking.com's API, have a look here
UPDATE
Booking.com DO have an XML API system, however as many people have stated it is not available to Developers. It is internal and only made available to Hotel/Chains who are apart of their partner system. So YES they do, but NO it's not publicly available.
Original Answer
I can categorically state that at the time of writing, Booking.com do not have an API system, I know this because I've contacted them requesting such info, and they kindly advised me that they do not have an API that is currently available to developers.