I'm going to throw caution to the wind and make another prediction ( see previous ) about Apple. I think that their new headless system is going to be a PVR (like TiVo).
First, though, let me explain why it's not going to be just a cheap iMac. Basically Apple has an image to maintain. Literally. Quality imaging is very important to the brand and to Jobs personally. The vast majority of PC monitors are not really up to the kind of quality video that Apple ships with their machines. They would have to go against their established principles to ship a Mac that's intended to run with third-party monitors.
On the other hand, there are several reasons why an Apple PVR makes sense.
1. The PVR is a successful product, but also one ripe for expansion into the mainstream. Apple can dominate.
2. Most people now have an integrated Audio/Visual setup, where the TV and the stereo are connected. An Apple PVR can serve as an iTunes hub for the iPod and connect with the stereo. And it would also integrate with iPhoto with the TV screen as a slide show viewer.
3. The iApps are adaptable to a TV screen resolution. That would include iTMS.
4. If Apple's going to make a Video iPod, where's the video going to come from? Why, the iPVR, of course. Video to go, as they say.
5. One more thing: look either now or in the near future for an iTMS-like store for downloading movies.
Form factor? The usual connections, plus some kind of TV tuner and A/V spots. The software form factor will need to be set up for low-rez display and remote control input device.