In my search for hotel APIs I have found only one API giving unrestricted open access to their hotel database and allowing you to book their hotels:
Expedia's EAN http://developer.ean.com/
You need to sign for their affiliate program, which is very easy.
You get immediate access to their hotel databases plus you can make availability/booking requests with several response options, including JSON, which is more convenient and lightweight than the (unfortunately) more widespread XML.
As you immediately access their API, you can start developing and testing, but still need their approval to launch the site, basically to make sure it provides the needed quality and security, which is reasonable.
They also offer "deep linking", i.e. you may customize your requests by adding parameters. Then if it sufficient for your purpose (for mine it is not), you don't even need to store their content on your server.
I have also signed for HotelsCombined program:
(link removed as this site doesn't seem to let me put more links)
However, they do not immediately allow you to use their API even for testing. From their answer:
"Apologies for the inconvenience caused, but it’s simply a business decision to limit access to our rich hotel content. Please kindly check back within the next 2-3 months, where we will be able to judge your traffic, and in turn judge your status on standard data feeds."
I have also signed for Booking.com affiliate program:
(link removed as this site doesn't seem to let me put more links)
Unfortunately, again, they limit access, from their answer:
"Please do note that, since there's a high amount of time and cost involved in the XML integration, we are only able to offer the XML integration to a small amount of partners with a high potential."
I did not explore Tripadvisor as they seem only to offer top 10 hotels and only as widgets, but most importantly for me, they wouldn't allow booking through them.
I've checked the hotelbase.org mentioned above, they have very extensive list but not as rich as by Expedia, also they don't seem to have images and don't allow booking either.