Amazon’s Fire TV Stick is a direct competitor to Google’s Chromecast, except that it runs a full version of Android.
The tiny device plugs into the back of your TV and enables you to stream content from various online sources, effectively turning any TV into a smart TV. A new version of the Stick has recently been released, although it represents only a minimal update over the original.
The Fire TV Stick can be rooted, but the question is whether it is worth it or not. The benefits are actually negligible. As an Android device, the ability to install apps from ‘Unknown Sources’ is in place, even if it isn’t readily accessible. Simply by using the Apps2Fire app (free) from the Google Play store you can install apps to the Stick by sending them from your phone. You will need to have the APK or you can’t install directly from the Play store.
However, the kinds of apps you would want to install, such as the excellent media streamer Kodi (formerly known as XBMC) can be added to the device with minimal technical knowledge. You can find more info on doing that on the official Kodi wiki.