http://www.sharedcount.com/
Edit: SharedCount has dropped support for many services, not so interesting now.

Nice details on the APIs available on various social networks:
http://www.codedevelopr.com/articles/get-social-network-share-counts/
https://developers.facebook.com/docs/insights/

And a JavaScript that handles it:
https://github.com/ritz078/socialShare.js

This is what a popular Wordpress addon is doing:
https://wordpress.org/plugins/facebook-share-statistics/

Just a quick note that this doesn't depend on any other social media work, e.g. with the Hybridauth addon.

It works on the basis of shared links, not syndicated content. And by definition it only needs to work with the most popular networks, as we want to track where things are spreading.