When first details were released regarding the Xbox One and Kinect, there were people likening the situation to 1984, with the ever-watching eye of the device constantly staring into the living room space.
Microsoft recently released their Xbox Privacy Statement, where they outline exactly how the data received by the Kinect will be stored and used. The succinct version of the post reads as follows:
Kinect creates a virtual gaming environment where your body motions and voice can be used to control gameplay and to navigate through the Service. Kinect uses an infrared sensor, camera, and microphone to make control possible.
The camera can be used to sign you in. To do so, it measures distances between key points on your face to create a numeric value that represents only you. No one could look at the numbers and know they represent you. This authentication information stays on the console and is not shared with anyone.
You control what happens to photographs taken during gameplay and whether voice commands are captured for analysis. You can turn Kinect off at any time.
When Kinect is used with certain games and apps, your skeletal movements can be used to estimate exercise stats. You can decide how your stats are managed and whether they are shared.
Some game titles may take advantage of a new Xbox capability called expressions. This feature allows you to use your defined facial expressions to control or influence a game. This data does not identify you, stays on the console and is destroyed once your session ends.
They also elaborate on how voice communications are monitored, in the process confirming that they do not listen in on Skype calls:
Kinect's microphones help enable chat and audio. Chat includes online voice talk between players during gameplay or talking to others using services such as Skype. You should not expect any level of privacy concerning your use of the live communication features such as voice chat, video and communications in live-hosted gameplay sessions offered through the Services.
We may monitor these communications to the extent permitted by law, but we cannot monitor the entire Service and make no attempt to do so. You understand that others can record and use these communications. Communications in live-hosted gameplay sessions may also be broadcast to others. Please note that Xbox does not listen in on Skype calls.