Booking.com Hotel Management API

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.

There are at least two third-party channel management services that say they can synchronize via API with booking.com among many other aggregators:
1) http://verticalbooking.com/en/channel_manager.htm

2) http://beds24.com/channel-manager.html

So, presumably, there is a way to interface via API with booking.com but how to do that directly without a third-party I don't know...