You should check out Simperium (disclaimer: I'm the co-founder and Twitter's former platform lead is one of our advisors/investors). While it's not immediately apparent yet, we're pushing in this direction: it's easy to create a firehose for your app, and we're working on ways for apps to easily interconnect with each other in a less file-centric, more API-centric way.
The niche we chose to start with is device syncing, based on our experience building Simplenote (which is to Evernote as Twitter is to Facebook). We know there's a need for something more flexible and powerful than iCloud in this regard, so that's what we focused on initially. But we believe a good solution for moving data between devices is also a good solution for moving data between people and 3rd-party apps.
Simplenote's 3rd-party ecosystem looks similar to Twitter's in the earlier days. We're taking the path they didn't take. Rather than shoring up Simplenote vertically, we're focused on extending our backend data layer horizontally and generalizing it for a variety of apps and services (though specifically not as an all-encompassing "backend-as-a-service"). We'll be announcing our open source strategy soon. This is all really hard though, both technically and as a business.