For quite a while, Google has been using its own goo.gl shortener to compress long links. No more; as of today, the big G is using a different shortener, g.co, for its own link-shortening needs.
The goal behind g.co is not to provide another URL shortener for you to create short links. Instead, it's a service that only Google can use to shorten links to its pages. That way, when you see a g.co link, you know that it's coming from a trusted source and you can click on it.
For your own links, you can still use Goo.gl. Just remember that when you see a g.co link around the internet, it's coming straight from Google and is safe to click on.