The following is only speculation - just for fun. I don't claim that any of it is accurate. However, since this page was first published (on Sunday October 1) the odds of the iPod movie becoming a reality have significantly increased with Apple's announcement of a media event on October 12.
Now that Apple has introduced iPod nano, they need to come up with more product differentiation for the hard drive-based classic iPod. The launch of nano also indicates a recognition on Apple's part that a lot of users don't need more storage space on their iPods - so to make an 80GB iPod into a compelling new product, they need to provide a new application for it.
The original vision for iPod photo was that you would hook it up to a TV and play slide shows on a big screen. Whilst the photo functionality proved fairly popular, (it's nice to browse through your photos whilst listening to music on the train,) the TV cable was (probably) not a big hit. Hence Apple merged their iPod photo and classic iPod lines - de-emphasised the photo functionality in their marketing, whilst introduced it into the nano, albeit without the TV connection.
The photo functionality proved to be more of a neat gimick than a killer app, but still handy as a point of differentiation and an argument to upgrade/upsell.
It's time for a new trick - and video could well be the solution, but not in the way that many people anticipate.
The problems with video on an iPod are obvious - no legal means of downloading video, and no real demand for video on a mobile device anyway. However, the same could be said of photos too, and that didn't stop them becoming a neat value-add. Apple are very likely to enable video in their iPods, just because they can (the hardware supports it anyway), and because it could differentiate. However, Apple produces "products" rather than gadgets. They won't want to introduce video just for the sake of it - they'll want make more of a proposition out of it.
The sales pitch will probably go something like this:

NB: When Apple finally have a Video Store ready to launch, we'll all know about it. It must still be a long way off, or otherwise it would surely have been included as part of iTunes 5. When it is ready (probably as part of a rebranded iTunes 6 - iMedia? ugh) Apple are more likely to market it together with a video-enabled Airport Express rather than with the iPod.
A larger screen will provide an enhanced user experience in a number of ways beyond video:

It also provides a platform for further feature enhancements:

iPod nano marked a shift back to the original iPod appearance - with sharp angled edged on the front, curved edges on the back, and a layer of transparent polycarbonate on the front surface. It's natural that this look will return to the classic iPod with the next update - although naturally in physically larger dimensions than the nano. For the purposes of these visuals, I've used the nano as the base, whilst make it appear thicker and larger. Nonetheless, it appears smaller than today's classic iPod.
In order to watch movies on an iPod with similar physical dimensions to today's iPod, it would be necessary to turn it 90 degrees for viewing. However, in order to retain the classic iPod ease of use, menus would still be navigated with the iPod held "portrait". The only weakness with this approach is that the click wheel button icons will be the wrong way round when watching video - I think this is probably an acceptable compromise. One possible solution would be to make the entire click wheel rotate - this could be enabled when you click and hold the play button - then turn it as if dialling a phone.
