DB's of that information is in itself a whole industry.
Travel websites are not small projects,so most people turn to 3rd party providers for booking engines.
Search for "booking engine" on google or yahoo you will see the responces.
Some require partnership, others hefty fee's
If you are serious about making a site a competitive booking engine be prepared to put up alot of investment in time and money.
If you are simply building a website for a travel agency and you need a flight/hotel booking, then you can simplly affiliate with any one of those "booking engine" sites, maybe even travelocity or expedia,and simply use their database. So your website will be "Powered by somesite..."