Use Chatter REST API to:
1. Build a mobile app.
2. Integrate a third-party web application with Salesforce so it can notify groups of users about events.
3. Display a feed on an external system, such as an intranet site, after users are authenticated.
4. Make feeds actionable and integrated with third-party sites. For example, an app that posts a 5. Chatter item to Twitter whenever the post includes #tweet hashtag.
6. Create simple games that interact with the feed for notifications.
7. Creating a custom, branded skin for Chatter for your organization.