The Japanese lunar orbiter "Kaguya" saw earth, moon and sun line up on April 6, 2008 and captured another "Earth-rise" and "Earth-set" HDTV video- this time when the Earth was full. (The original November videos were taken when the Earth was wanning (not quite full).
According to JAXA the line up occurs only twice a year and allows the orbiter to take these movies as it comes from around the back side of the moon and into view of the Earth. If you haven't worked out how that happens (I haven't either), the Japanese Aerospace Exploration Agency (JAXA) has kindly provided a diagram.
For the Earth to look "full" the moon has to be between the earth and the sun and looking at the fully illuminated Earth. When the moon is between the Earth and the sun it would be a New Moon (since we on Earth are looking at its unilluminated side). The moon doesn't block the sunlight from falling on Earth since it's small and orbiting at a 5 degree tilt to the plane of Earth's orbit, so it is usually above or below the line of sight of the sun - see animation link below.) If you look at a lunar calendar April 6th was New Moon and the day these videos were taken.
Now, there is a New Moon every month, so why can it only capture the "Full Earth" twice a year? Check out this link for a cool animation of the moon orbiting the Earth from the perspective of the sun to help visualize why the moon only lines up directly with the earth and the sun twice a year. The animation gives a good sense of why lunar eclipses only happen twice (or four times) a year, but I am not clear about how that relates to Earth's fullness. I welcome comments from people who really know.
Note that the Apollo missions picture of "Earth-rise" did not happen to fall during "full-Earth" and had an Earth that was about 3/4's full. JAXA thinks this is the first full Earth picture to be captured, if not, it certainly is the first full Earth captured in HDTV...
JAXA has a beautiful flash site of the images it has taken with Kaguya. They also have a gallery of HDTV videos from Kaguya that are easier to navigate if you can read Japanese. The HDTV videos are not full resolution. JAXA has not released those versions yet. It is believed that their partner, the Japanese Public Broadcasting Corporation (NHK) are reserving them for future commercial and educational purposes.