All of the Contour cameras have a lens bezel (the outer ring of the camera's lens) that rotates. This means that you can turn the camera's lens to stay upright even when the camera body is mounted as an off angle.
The ContourHD 720p, ContourHD 1080p, and ContourGPS all have lens bezels that will rotate 180°. The Contour+ and ContourROAM have lens bezels that will rotate 270°.
To rotate the the lens bezel, grip the camera body in one hand and turn the lens bezel in the other. It may be a little stiff at first, but don't worry. The lens bezel is designed to rotate.