Hyperlinks allow you to seamlessly browse the Web - clicking on a link in an email inside your webmail client can transport you to an article on Wikipedia which can lead you to a reference on some other website. Hyperlinks provide the glue which keeps the Web together. They link the vast amounts of information the Web has to offer together and allow for one, seamless interaction.
With apps we are silo’ed - none of the apps on my phone, my tablet and for the most part on my computer link together in this seamless way. If a photo app on my iPhone wants to share the picture I just took on Twitter it needs to implement this functionality internally - regardless if I have the Twitter app installed on my phone or not. Developers are forced to reinvent the wheel all the time. Users can't easily link their preferred apps together (what if I don't use Twitter but Identi.ca or store my photos on SmugMug and not flickr?)
APIs provide this capability - but they strongly favor a highly concentrated distribution model: As every developer needs to implement each API again and again, developers only integrate with the biggest players in the market.
The future should consists of a simple, unified API (let's call it - for lack of a better word - the “API-to-Me”) which provides a way for each of your apps to announce which data and functionality it can provide -- and consequently consume these services from your other apps. The user agent (your browser) acts as the intermediary - putting you (the user) squarely into the middle of this exchange: At all times do you stay in full control over which apps shares data & services with any other app.