#Images (of movie clips) used as background in the 3D viewport will not render.
Here are a couple of alternatives:
Using the compositor
To add an Input>Movie Clip node, and use an alpha over node to compose the render layers over it.
For single images use an Input>Image node.
If youare using cycles make sure that you enable Film Transparent, so that the rendered layers render with a transparent background:
As an Alternative
Without using additional geometry or compositing, you can use the image as background for the world. Set the Texture coordinates to Window.
