We have an open and pretty well documented API (https://gimmebar.com/api/v1), which is basically what we use to build the Dropbox export in addition to the Instagram, Pinboard, etc. backups. We chose Dropbox because the intersection of our users and Dropbox users is quite high, and it was simple enough to execute.

You could very easily build a simple application to back up all of your data to whatever service (S3, personal server, Some Other Cloud™).