Using the Shotgun API it's very possible to integrate with a number of third party packages, however there are a few with which Shotgun integrates right out of the box.
RV and Screening Room
At it's most basic level, RV integration with Shotgun allows for right-click "Play in RV" functionality from Versions within Shotgun. With the release of Screening Room, RV and Shotgun have become a more powerful platform for review and approval.
Cinesync allows you to have simultaneous synced playback between multiple locations. Shotgun's integration allows you to create a Playlist of Versions, play it in Cinesync, and send your Notes made during the session right back into Shotgun.
The Shotgun+Deadline integration allows you to automatically submit rendered Versions to Shotgun complete with thumbnail, links to frames, and other metadata. An overview is provided here but complete docs and info are available on the Deadline website.
Much like the Deadline integration, the Shotgun+Rush integration allows you to automatically submit rendered Versions to Shotgun complete with thumbnail, links to frames, and other metadata.
We have a light but flexible integration (that we use internally) that allows us to track revisions and link them to tickets and releases in Shotgun. We also provide links to Trac to integrate with an external web svn repository viewer. This is all done pretty simply by adding a post-commit hook to SVN which is a Shotgun API script that takes some ENV variables from the commit and then creates a Revision entity in Shotgun with various fields filled in. It can be modified to match your studio's needs and can be used for a local or hosted installation since it's just using the API.