This is solution for Original Kinect for Windows. If you are looking for solution for Kinect V2 you need to go to my recent post about that at KinectCamV2.
To install get
New.KinectCam ver. 1.2 (27448 downloads) or New.KinectCam ver. 1.2 HD (24598 downloads), unpack, run install.bat as Administrator. Version 1.2 has freeze bug fixed and there is new version that support HD mode in 1280×960 resolution.
New.KinectCam ver. 1.1 (18160 downloads), unpack, run install.bat as Administrator. Version 1.1 has Angle option in settings, so you can change angle of Kinect camera and it is automatically saved. To change Angle setting open in Skype Tools->Options->Video Camera and go to Webcam Settings for Kinect Camera. On Settings window change position of Angle control and this will be automatically saved for next usage of Kinect Camera. It works also with Skype for Business 2015. UPDATE: Please edit both install.bat and uninstall.bat and change from .NET 2.0 directory into .NET 4.0 directory, because Skype was updated to .NET 4.0 some time ago. Enjoy!
New.KinectCam (26215 downloads), unpack, run install.bat as Administrator. You need Kinect for PC device and Kinect Runtime 1.6 or Kinect SDK 1.6. or you can use Kinect Runtime 1.7 or Kinect SDK 1.7 or Kinect SDK 1.8 as well :). It is pure C#/.NET 2.0 implementation!