A lot of people are trying to fix this right now. A lot of people think that most API's, even though guided by Oauth or Oauth 2.0, are easy to implement, and it's a huge misconception. So many of the API's have quirks and issues all the time, making it incredibly time consuming to implement, learn, and keep up to date.
Making the process easier is a huge need right now. There are a lot of apps, and it's all becoming more separated. People want to integrate, and it's a pain in the ass to integrate quickly and cleanly.
EmergentOne and Apigee are helping people create standard API's.
Zapier and IFTTT are giving you a UI to meld them together.
Cloudsnap, Singly, and Webshell are all doing what you're describing, each with a different target of apps. Singly and Webshell are seemingly more social, whereas Cloudsnap is more related to business apps.
And of course, YQL, which has been around a long time.
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Disclosure: I'm a designer for Cloudsnap, and above is my opinion and not necessarily the views of the company.
http://pi.pe/ might be able to handle those transfers. I haven't looked into it too much and I'm not sure what the experience is like, but I have seen it posted several times for that type of request. Might want to check it out.