The 4sync SOAP API provides over 50 API functions like uploading and downloading files and deleting folders. The API gives access to 4sync's cloud synching, which is acknowledged to be among the least expensive deals available, featuring 15 gigabytes of free storage.
There are now a number of backend-as-a-service companies focused on mobile developers. We list 6 backend APIs that help with common mobile tasks, including the Cocoafish API, which was today acquired by Appcelerator. But it's a much bigger ecosystem, as shown in the infographic below.