The original Apple iPod video cable - the one that plugs into the headphone jack - only works on video-capable iPods through the 5.5 gen iPod.
When the iPod Classic and the 3rd generation Nano were introduced, it began the requirement for a new video cable - one which plugs in through the dock connector instead of the headphone jack. This applies to the iPod Touch and the iPhone as well. The new cable incorporates an "authentication" chip, too - probably due to licensing issues with the movie companies, so that movies could be offered for sale or rental while supposedly minimizing the chances for illicit copying.
Incidentally, the newer video-capable iPods are also capable of higher-quality COMPONENT video (red, green and blue plugs) as well as the usual COMPOSITE video (yellow plug). This, of course, requires a different cable with the aforementioned dock connector.