That would be search. It allows you, the user, to find information and content you need and want, fast. Google gets that, and they serve your ads with it. Search also allows a site owner to figure out what people are looking for - there are services like Lijit that give you a snapshot of what people looked for on your aggregated content.
Take publications with great content and deep, digital archives, and you can see why. There are already a few search APIs out there - the New York Times announced one recently, so did NPR and TechCrunch. [hat tip to Jeff Jarvis]
If you scroll down on the Daylife page, you will see the corner dedicated to the API. One cool thing I like about their implementation is that it, like Lijit and other search APIs, allow you to see what others have found interesting. Given that peer to peer impressions are much more powerful than any content source alone, transparency in that function is a bonus.
Will the use of APIs change news? Has news changed on the basis of readers and listeners comments? What will you do with the data? How do you use the search results of your publication? Do you feed them back into the way you plan content and what your business offers?
Take a practical application for entrepreneurs - patents. There is a Google AJAX Patent Search API you can use. I am also intrigued by Jarvis' question. If you could access any data through APIs, what would you want to access and what would you do with that data?
If search is an important function, what you do with the results, the data? Will it help you take your business forward? How would you go about it? We have gotten really good at collecting and amassing enormous amounts of data. What stories will emerge when the data is actionable?